One of the most enlightening things that St. Thomas says about faith, is that nothing false can come under faith:

Quote from: St. Thomas

I answer that, Nothing comes under any power, habit or act, except by means of the formal aspect of the object: thus color cannot be seen except by means of light, and a conclusion cannot be known save through the mean of demonstration. Now it has been stated (1) that the formal aspect of the object of faith is the First Truth; so that nothing can come under faith, save in so far as it stands under the First Truth, under which nothing false can stand, as neither can non-being stand under being, nor evil under goodness. It follows therefore that nothing false can come under faith.

This startles us because we are used to talking about faith, not as a divine light which unfailingly reveals the Truth, but as a strong conviction, a subjective belief - we talk about the "Protestant faith", the "Jєωιѕн faith", the "Islamic faith", the "Hindu faith", when in fact, there is no other faith properly speaking, than the divine Catholic faith which proceeds from God through the Church. This is how faith can be infallible, never teaching anything false - because faith proceeds from the Catholic Church, which itself is infallible, being taught by God, who can neither deceive nor be deceived.

If a Catholic accidentally believes in something against the Catholic faith (e.g. he believes that Mary is not a perpetual virgin), he is said to have implicit faith in that article of faith, if he is ignorant that the Church teaches it. If, after being told that the Church teaches it, he does not submit to the teaching of the Church, then he does not have faith, because faith proceeds from the Church and requires submission to its teaching authority, and his refusing to submit shows that he is faithless heretic. However, if, after being told that the Church teaches it, he immediately assents to the teaching of the Church, this shows that he does indeed submit his mind to the Church, and that he did have an implicit faith in that article, which was implicit rather than explicit due to ignorance. This is the original usage of the "implicit faith", for Catholics who knew the basic articles of faith but not every Church teaching.

Here is an ancient example of how implicit faith works:

Quote from: Sayings of the Desert Fathers

This is what Abba Daniel, the Pharanite, said, ‘Our Father Abba Arsenius told us of an inhabitant of Scetis, of notable life and of simple faith; through his naivete he was deceived and said, ‘The bread which we receive is not really the body of Christ, but a symbol.’

 Two old men having learnt that he had uttered this saying, knowing that he was outstanding in his way of life, knew that he had not spoken through malice, but through simplicity. So they came to find him and said, ‘Father, we have heard a proposition contrary to the faith on the part of someone who says that the bread which we received is not really the body of Christ, but a symbol.’

 The old man said, ‘It is I who have said that.’

 Then the old men exhorted him saying, ‘Do not hold this position, Father, but hold one in conformity with that which the catholic Church has given us. We believe, for our part, that the bread itself is the body of Christ and that the cup itself is his blood and this in all truth and not a symbol. But as in the beginning, God formed man in his image, taking the dust of the earth, without anyone being able to say that it is not the image of God, even though it is not seen to be so; thus it is with the bread of which he said that it is his body; and so we believe that it is really the body of Christ.’

The old man said to them, ‘As long as I have not been persuaded by the thing itself, I shall not be fully convinced.’

So they said, ‘Let us pray God about this mystery throughout the whole of this week and we believe that God will reveal it to us.’

The old man received this saying with joy and he prayed these words, ‘Lord, you know that it is not through malice that I do not believe and so that I may not err through ignorance, reveal this mystery to me, Lord Jesus Christ.’

The old men returned to their cells and they also prayed God, saying, ‘Lord Jesus Christ, reveal this mystery to the old man, that he may believe and not lose his reward.’

God heard both the prayers. At the end of the week they came to church on Sunday and sat all three on the same mat, the old man in the middle. Then their eyes were opened and when the bread was placed on the holy table, there appeared as it were a little child to these three alone. And when the priest put out his hand to break the bread, behold and angel descended from heaven with a sword and poured the child’s blood into the chalice. When the priest cut the bread into small pieces, the angle also cut the child into pieces. When they drew near to receive the sacred elements the old man alone received a morsel of the bloody flesh. Seeing this he was afraid and cried out, ‘Lord, I believe that this bread is your flesh and this chalice your blood.’ Immediately the flesh which he held in his hand became bread, according to the mystery and he took it, giving thanks to God.

 Then the old men said to him, ‘God knows human nature and that man cannot eat raw flesh and that is why he has changed his body into bread and his blood into wine, for those who receive it in faith.’ Then they gave thanks to God for the old man, because he had allowed him not to lose the reward of his labor. So all three returned with joy to their own cells.

The man did not believe the truth in regards to the Blessed Sacrament, but he did not obstinately reject that truth either. In my opinion, it should have been enough for him to learn that the Catholic Church teaches this truth in order for him to give his assent, but this comes from the ancient desert fathers who perhaps were not as in touch with the infallible Magisterium. Nevertheless, this amply demonstrates the concept of implicit faith for Catholics who err out of ignorance of certain articles, but who do not obstinately cling to their error, as do heretics.

Now, given that nothing false can come under faith, it is enough to show that a man clings obstinately to something false to demonstrate that he is without faith. For example, if a Protestant obstinately rejects the Assumption or the Real Presence, he is without faith. If an Orthodox obstinately rejects the Immaculate Conception or the Filioque, he is without faith. These are heretics who do not have divine faith proceeding from God through the Catholic Church, but human opinion proceeding from their own minds or the minds of other men. The same, of course, is true of Jєωs and Muslims who obstinately reject even the first articles of faith. The Protestants and Orthodox have an advantage to Jєωs, Muslims, and pagans, in that they have "preambles to the faith", in fact, the Orthodox practically have every article of faith, but without the divine authority which reveals it. Subjectively, they are closer to the Catholic faith, but objectively they do not have it.

The Catholic faith is not the best of human opinions, it is the divine light itself made manifest to the world through the teaching of the Catholic Church. This is why the Catholic Church is so necessary for salvation.

The authoritative docuмents of the teaching Church cited in the first part of this book, particularly the Holy Office letter Suprema haec sacra, have made it abundantly clear that, according to God’s revealed message, it is not necessary to be a member of the Catholic Church at the moment of death in order to attain to the Beatific Vision.  We know that under certain circuмstances a man may be saved if, at the moment of his death, he is not actually a member of the Church but only one who intends or wills to be within it.  We know also that this desire or intention of entering the Church can be effective for the attainment of eternal salvation even when it is only implicit.

   The Suprema haec sacra explains this truth in terms of the fact that the Catholic Church, like the sacrament of baptism, is requisite for the attainment of the Beatific Vision, not by any intrinsic necessity, but by reason of God’s own choice or institution.  Now, when we are considering the adequate concept of the Lord’s true ecclesia in terms of its necessity for the attainment of salvation, we should examine this portion of the Catholic doctrine about it.

   A thing is said to be necessary for salvation with an intrinsic necessity when this thing is an essential element or factor in the life of sanctifying grace to which the Beatific Vision itself belongs.  Thus divine charity is intrinsically necessary for salvation.  The affection of charity is the love of friendship for God as He is known supernaturally, in the Trinity of His Persons.  Thus the love of charity is essentially a part of the life of the Beatific Vision both in heaven and here in this world.  Where such a love does not exist, the life of the Beatific Vision, the life of sanctifying grace, does not exist.

   Genuine supernatural faith, that virtue by which we accept the truths God has revealed as perfectly certain precisely on His authority, is an essential part of the life of sanctifying grace during its preparatory status in this world.  There can obviously be no such thing as a supernatural life with reference to God, known in the Trinity of His Persons, apart from an awareness of Him in this way.  In the patria of heaven, those who belong to the Church triumphant understand the Triune God in the Beatific Vision itself.  But the Beatific Vision is precisely the reward of, the thing merited in, the life of grace in this world.  The passion of the Beatific Vision is incompatible with the status of one in the Church militant.

   The Beatific Vision is the direct, intuitive, and clear understanding of the Blessed Trinity.  And, apart from the Beatific Vision itself, the only certain knowledge or apprehension of the Blessed Trinity and of the supernatural order that centers around the Blessed Trinity is to be found in the acceptance of a supernaturally revealed message about the realities of this order.  The certain acceptance of that body of revealed truth, made possible by the gift of God’s grace, is the assent of divine faith.  Thus faith is absolutely requisite for the living of the supernatural life of grace in its preparatory status in this world.  And, because only those who have passed from this life living the life of sanctifying grace can attain to the Beatific Vision, faith is absolutely necessary for the attainment of eternal salvation.

   As a result, there can be no such thing as any substitute for the actual possession of faith and hope and charity as requisites for the attainment of the life of heaven.  A man could not be saved if he were to have faith and charity merely in desire or intention at the moment he passed from this life.  A desire or willingness to believe with the act of faith or to love God with the affection of charity definitely would not and could not take the place of faith and charity themselves.  If a man is to attain eternal salvation he must possess genuine supernatural faith and the true and supernatural love of charity at the moment of his death.

   Now, faith and hope and charity are factors or elements entering into the composition of the Catholic Church itself.  Together they constitute what the older theologians called the inward or spiritual bond of unity within the Church, joining men to God and to each other within this company.  Furthermore, they are intrinsically or absolutely necessary as components of God’s supernatural kingdom on earth.  There could be no such thing as the ecclesia, the people of the Covenant, the company of men and women who subject themselves to the divine law directing them to the supernatural end of the Beatific Vision apart from the acceptance of that supernatural message in faith and obedience to it in charity.

   Furthermore, faith, hope and charity are completely inseparable from the ecclesia as factors uniting those who belong to the supernatural kingdom of God on earth with one another.  There could be no such thing as a social unit identifiable as the true Church of Jesus Christ apart from the inward or spiritual bond of union of faith and hope and charity.

   In the composition of the Church militant of the New Testament there are, however, two distinct bonds of unity, two sets of forces tending to unite men to God and to each other in Jesus Christ.  Besides this inward or spiritual bond, there is another, designated by some of the classical theologians as the outward or bodily bond of unity within the true Church.  This outward bond consists in the baptismal profession of the faith, access to or communion in the sacraments, and subjection to the legitimate pastors of the Church.

   This second or outward bond of union within the true Church is something made necessary in the supernatural life only because of God’s free choice.  None of its elements, taken in themselves, are necessarily parts of the life of sanctifying grace.  There could have been an ecclesia, a supernatural kingdom of God on earth, in which these elements would not have entered.  And, as a matter of fact, during its various Old Testament stages, God’s ecclesia on this earth did not contain the factors which go to compose the outward bond of ecclesiastical unity in the Church militant of the New Testament.

   These factors actually belong to the composition of the true ecclesia in its final status in this world only because God, in His infinite wisdom and mercy, freely decreed that they should do so.  He established His supernatural kingdom of the New Testament as a visible and organized society.  He constituted it with this definite set of factors which go to make up the outward or visible bond of unity within it.  He formed His Church of the New Testament in such a way that membership in it depended entirely on the possession of that outward bond of ecclesiastical unity.

   Because the factors that enter into membership in the Church militant of the New Testament belong to the composition of the true ecclesia only by reason of God’s free choice, and not because they enter into the actual life of sanctifying grace, it has pleased God in His goodness and mercy to allow men to have the benefits of this membership when it is really impossible for them to attain the membership in itself and when they sincerely desire to enter and to remain within His ecclesia.  If there is a sincere and supernatural will to come and to stay within the true Church of Jesus Christ, the man who has that desire will realize that the good he seeks is something only God will be able to give.  The expression of that desire to God in the form of a petition is the act of prayer.

   Now prayer, the act of worship which consists in the petition of fitting things from God, is infallibly efficacious, according to Our Lord’s own promise. [Cf. Mark, 11: 24; John, 16: 23.]  It is infallibly effective for the attainment of the individual benefits sought in it when certain conditions have been fulfilled.  The prayer must be said for one’s self, and must seek either eternal salvation of something necessary for the attainment of salvation if it is to obtain its effect without fail.  It must also be pious, that is, enlightened by true divine faith and motivated by the theological act of hope and by some supernatural love of benevolence for God.  Finally, it must be persevering, that is, it must be the expression of a genuine desire or will of the person offering the prayer.  [Cf. Fenton, The Theology of Prayer (Milwaukee: The Bruce Publishing Co., 1939), pp. 206-15.

   When a man desires or prays for entrance into the true Church of Jesus Christ, even when this objective is apprehended only in an implicit way by the person praying, the first two of these conditions are necessarily fulfilled.  The prayer is offered for the person himself, and it seeks a good which is truly requisite for the attainment of eternal salvation.  In order that this prayer for entrance into the Church may be effective for salvation, the prayer and the intention behind it must be enlightened by faith and motivated or animated by charity.  And it must also be a persevering prayer.

   If a person who is praying in this way should die before he can actually become a member of the Church, then by the very force of his prayer, he will die as one contained “within” the Church by will or desire.  And if the person who is praying in this way dies loving God and his neighbor with the love of charity, that person leaves this world “within” the true Church of Christ on earth and will remain in the Church triumphant for all eternity.

   It must not be imagined that such an individual has his prayers answered only by the granting of a fictitious connection with the true ecclesia.  The individual who accepts God’s supernatural revelation with the certain assent of faith and who loves God with the affection of charity is actually and necessarily ordering his conduct in accord with the corporate activity of the true Church itself.  We must never lose sight of the teaching about the nature of the true Church set forth in the opening passage of Pope Leo’s encyclical Humanum genus if we are to understand this section of Catholic doctrine.  According to that docuмent, the kingdom of God, which is the true Church of Jesus Christ, “steadfastly contends for truth and virtue” in such a way that “those who desire from their heart to be united with it so as to gain salvation must of necessity serve God and His only-begotten Son with their whole mind and with an entire will.”  [The Great Encyclical Letters of Pope Leo XIII, p. 83.]

   Now, it is the basic contention of that part of Catholic doctrine presented in this passage of Pope Leo XIII’s encyclical that this work of God’s supernatural kingdom in this world is continuously and bitterly opposed by the kingdom of Satan.  The non-member of the Church who has faith and charity and who sincerely desires to enter the Church has organized his life to fight on the side of the ecclesia for the objectives which the ecclesia seeks.

   It must be remembered that God’s supernatural kingdom here on earth has no corporate allies in its warfare against the kingdom of “the prince of this world.”  There is not, and there never will be, another social unit fighting alongside the true Church for the attainment of those ends for which the Church contends.  If a man really fights for truth and virtue, if he really works to serve and to glorify the Triune God, then he is fighting on the side of, and in a very real sense “within,” the true Church itself.

   And, if a man really has divine charity, he is actually fighting this battle for the Church.  The virtue of charity is the ultimate motivating force in the life and conduct of the man who possesses it.  It is something intensely and essentially active.  If a man really loves God with the affection of charity, his activity is necessarily directed toward the objective of pleasing God.  If, on the other hand, a man is not working to please God, to glorify and serve Him, this man does not truly love God with the love of charity.

   The situation of the person who is not a member of the Church, but who is “within” it by intention, desire or prayer, can be understood best in comparison with the condition of a Catholic in the state of mortal sin.  Despite the fact that he is a member of the society which “steadfastly contends for truth and virtue,” this individual’s will is turned away from God and strives for objectives opposed to those sought by the Church.  He is one of those “who refuse to obey the divine and eternal law, and who have many aims of their own in contempt of God, and many aims also against God.”  In other words, in spite of his membership in the supernatural kingdom of God on earth, he is actually working and fighting for the things the kingdom of Satan seeks.

   The ultimate orientation of a man’s activity comes from the supreme intention of his will.  For the man in the state of grace, this supreme intention is the love of charity.  It is the desire to please God in all things.  The man in the state of mortal sin has some other supreme objective.  There is some end he seeks in contempt of God.  Even though some of his acts are good in themselves, ultimately his life is directed to the attainment of that end, which is the purpose of the kingdom of Satan.

   If a member of the Church should die in the state of mortal sin, he will be condemned forever to hell, the homeland of Satan’s kingdom.  He will, in other words, be assigned forever to the social unit in which and with which he was fighting at the moment of his passage from this life.  In exactly the same way, the non-member of the Church who dies believing God’s message with the assent of faith, loving God with the affection of charity, and sincerely willing and praying to enter God’s ecclesia, will live forever in the social unit within which he willed and prayed to live and for which he was fighting at the moment of his death.  Fenton - 1958