The Dogma of Infallibility
It is a dogma of the Catholic Church that the Church is divinely kept from the possibility of error in her definitive teaching on faith and morals.
Definition of “Infallibility” from “A Catholic Dictionary”, 1951: "This infallibility resides (A) in the pope personally and alone; (B) in an ecuмenical Council subject to papal confirmation (these infallibilities are distinct but correlative); (C) in the bishops of the Church, dispersed throughout the world, teaching definitively in union with the pope. This is not a different infallibility from (B) but is the ordinary exercise of a prerogative (hence called the "ordinary magisterium") which is manifested in a striking manner in an ecuмenical Council. This ordinary magisterium is exercised by pastoral letters, preaching, catechisms, the censorship of publications dealing with faith and morals, the reprobation of doctrines and books: it is thus in continuous function and embraces the whole deposit of faith."
The Catholic Encyclopedia (1917) in the article on Infallibility, states the same: "Three Organs of Infallibility: 1. the bishops dispersed throughout the world in union with the Holy See (exercised by what theologians describe as the ordinarium magisterium, i. e. the common or everyday teaching authority of the Church), 2. ecuмenical councils under the headship of the pope; and 3. the pope himself separately.
So these definitions coincide with the magisterium definitions above.
In other words, teaching from the Ordinary Magisterium continually occurs throughout the Church century after century, and the decisions of Popes and Councils (Solemn Magisterium) confine what is taught through the ordinary teaching. Both solemn and ordinary teaching of the Church are considered infallible by this definition. The infallibility of both Solemn and Ordinary Magisterium was solemnly defined by the First Vatican Council (1870) when it stated the following:
"All those things are to be believed by divine and Catholic faith which are contained in the written Word of God or in Tradition, and which are proposed by the Church, either in solemn judgment or in its ordinary and universal teaching office, as divinely revealed truths which must be believed."
In other words, both forms of the Magisterium of the Church (Solemn or Ordinary) are infallible and must be believed, according to this General Council. So if a teaching in the Church is universal, and allowed to propagate without condemnation from the Solemn Magisterium, it is considered infallible by the First Vatican Council. Next we provide examples of such teaching from both solemn and ordinary teaching of the Church on the subject of the threefold Baptism.