43. In the same way, actually that baptism is the distinctive mark of all Christians, and serves to differentiate them from those who have not been cleansed in this purifying stream and consequently are not members of Christ, the sacrament of holy orders sets the priest apart from the rest of the faithful who have not received this consecration.

The teaching of St. Augustine is so full that it might well fill a volume. The Church is the body of Christ and the Holy Ghost is the soul of that body ; for the Holy Ghost does in the Church all that the soul does in all the members of one body ; hence the Holy Ghost is for the body of Jesus, which is the Church, what the soul is for the human body. Therefore if we wish to live of the Holy Ghost, if we wish to remain united to him, we must preserve charity,love truth, will unity, and persevere in the Catholic faith ; for just as a member amputated from the body is no longer vivified by the soul, so he who has ceased to belong to the Church receives no more the life of the Holy Spirit. 4 " The Catholic Church alone is the body of Christ . . . outside that body the Holy Spirit gives life to no man . . consequently those who are outside the Church have not the Holy Spirit." 5 " His body is the Church, not this Church or that Church, but the Church throughout the whole world ; . . .for the whole Church, consisting of all the faithful, since all the faithful are members of Christ, has in Heaven that Head which rules his body." 6 In his De Unitate Ecclesiae (2), he tells us that " the Church is the body of Christ, as the Apostle teaches. 7 Whence it is manifest that he who is not a member of Christ cannot share in the salvation of Christ.

XavierSem cited the Catechism of St. Pius X, but the Catechism is merely referring to people who are "on the way of (or path to) salvation" being drawn by the Holy Spirit, and that is in fact the teaching of the Council of Trent, that the Holy Spirit (which Pius XII taught is the soul of the Church) draws them toward the Church even while they remain outside.

5.
(. . .)
Another head like to Christ must be invented – that is, another Christ if besides the one Church, which is His body, men wish to set up another. “See what you must beware of – see what you must avoid – see what you must dread. It happens that, as in the human body, some member may be cut off a hand, a finger, a foot. Does the soul follow the amputated member? As long as it was in the body, it lived; separated, it forfeits its life. So the Christian is a Catholic as long as he lives in the body: cut off from it he becomes a heretic – the life of the spirit follows not the amputated member” (S. Augustinus, Sermo cclxvii., n. 4).

The Church of Christ, therefore, is one and the same for ever; those who leave it depart from the will and command of Christ, the Lord – leaving the path of salvation they enter on that of perdition. “Whosoever is separated from the Church is united to an adulteress. He has cut himself off from the promises of the Church, and he who leaves the Church of Christ cannot arrive at the rewards of Christ….He who observes not this unity observes not the law of God, holds not the faith of the Father and the Son, clings not to life and salvation” (S. Cyprianus, De Cath. Eccl. Unitate, n. 6).

Upon the mountain of the Catholic Faith, which the sincere devotion of the disciples of Christ–boiling with the fire of charity–has thoroughly taught with the word of solicitous preaching to the peoples of the nations who walked in shadows, and which the Roman Church holds and guards, the solid foundation of the Christian religion is recognized to have been placed, never to be shaken by any disturbance, never to be violently shaken by the commotion of any storm. For indeed this is the Right, and True Faith, without the familiarity of which no one welcome is brought into the sight of the Most High, no one gracious is encountered. This is that, which prepares the path of salvation, and which promises the rewards and joys of eternal felicity.

10. (. . .) And the Church is where Peter is, and Peter speaks in the Roman Pontiff, living at all times in his successors and making judgment, providing the truth of the faith to those who seek it. The divine words therefore mean what this Roman See of the most blessed Peter holds and has held.

11. For this mother and teacher of all the churches has always preserved entire and unharmed the faith entrusted to it by Christ the Lord. Furthermore, it has taught it to the faithful, showing all men truth and the path of salvation.