The Vatican Council
Fourth Session, Chapter 2 
ON THE PERMANENCE OF THE PRIMACY OF BLESSED PETER IN THE ROMAN PONTIFFS
That which our lord Jesus Christ, the prince of shepherds and great shepherd of the sheep, established in the blessed apostle Peter, for the continual salvation and permanent benefit of the church, must of necessity remain for ever, by Christ's authority, in the church which, founded as it is upon a rock, will stand firm until the end of time [45].
For no one can be in doubt, indeed it was known in every age that the holy and most blessed Peter, prince and head of the apostles, the pillar of faith and the foundation of the catholic church, received the keys of the kingdom from our lord Jesus Christ, the saviour and redeemer of the human race, and that to this day and for ever he lives and presides and exercises judgment in his successors the bishops of the holy Roman see, which he founded and consecrated with his blood [46].
Therefore whoever succeeds to the chair of Peter obtains by the institution of Christ himself, the primacy of Peter over the whole church. So what the truth has ordained stands firm, and blessed Peter perseveres in the rock-like strength he was granted, and does not abandon that guidance of the church which he once received [47]. For this reason it has always been necessary for every church--that is to say the faithful throughout the world--to be in agreement with the Roman church because of its more effective leadership. In consequence of being joined, as members to head, with that see, from which the rights of sacred communion flow to all, they will grow together into the structure of a single body [48].
Therefore, if anyone says that it is not by the institution of Christ the lord himself (that is to say, by divine law) that blessed Peter should have perpetual successors in the primacy over the whole church; or that the Roman pontiff is not the successor of blessed Peter in this primacy: let him be anathema.
45. See Mt 7, 25; Lk 6, 48
46. From the speech of Philip, the Roman legate, at the 3rd session of the council of Ephesus (D no. 112).
47. Leo 1, Serm. (Sermons), 3 (elsewhere 2), ch. 3 (PL 54, 146).
48. Irenaeus, Adv. haeres. (Against Heresies) 1113 (PG 7, 849), Council of Aquilea (381), to be found among: Ambrose, Epistolae (Letters), 11 (PL 16, 946).