The Papacy
We also define that the holy apostolic see, and the Roman pontiff, holds the primacy over the whole world, that the Roman pontiff is the successor of blessed Peter, prince of the apostles, that he is the true vicar of Christ, the head of the whole Church and the father and teacher of all Christians, and that to him was committed in blessed Peter the full power of tending, ruling and governing the whole church, as is contained also in the acts of ecumenical councils and in the sacred canons (COUNCIL OF FLORENCE, 1439).
Therefore, faithfully adhering to the tradition received from the beginning of the christian faith, ... we teach and define as a divinely revealed dogma that when the Roman Pontiff speaks ex cathedra, that is, when, in the exercise of his office as shepherd and teacher of all Christians, in virtue of his supreme apostolic authority, he defines a doctrine concerning faith or morals to be held by the whole Church, he possesses, by the divine assistance promised to him in blessed Peter, that infallibility which the divine Redeemer willed his Church to enjoy in defining doctrine concerning faith or morals. Therefore, such definitions of the Roman Pontiff are of themselves, and not by the consent of the Church, irreformable (VATICAN COUNCIL I, 1870).