Council of Chalcedon
"After the reading of the foregoing epistle [The Tome of Leo], the most reverend bishops cried out: ‘This is the faith of the fathers! This is the faith of the apostles! So we all believe! Thus the orthodox believe! Anathema to him who does not thus believe! Peter has spoken thus through Leo! . . . This is the true faith! Those of us who are orthodox thus believe! This is the faith of the Fathers!’" (Acts of the Council, session 2 [A.D. 451]).

"Bishop Paschasinus, guardian of the Apostolic See, stood in the midst [of the Council Fathers] and said, ‘We received directions at the hands of the most blessed and apostolic bishop of the Roman city [Pope Leo I], who is the head of all the churches, which directions say that Dioscorus is not to be allowed to sit in the [present] assembly, but that if he should attempt to take his seat, he is to be cast out. This instruction we must carry out" (Acts of the Council, session 1 [A.D. 451]).

Council of Sardica
"[I]f any bishop loses the judgment in some case [decided by his fellow bishops] and still believes that he has not a bad but a good case, in order that the case may be judged anew . . . let us honor the memory of the apostle Peter by having those who have given the judgment write to Julius, Bishop of Rome, so that if it seem proper he may himself send arbiters and the judgment may be made again by the bishops of a neighboring province" (canon 3 [A.D. 342]).
"[I]f some bishop be deposed by the judgment of the bishops sitting in the neighborhood, and if he declare that he will seek further redress, another should not be appointed to his see until the bishop of Rome can be acquainted with the case and render a judgment" (canon 4).
 
  Pope Gregory I
"Your most sweet holiness, [Bishop Eulogius of Alexandria], has spoken much in your letter to me about the chair of Saint Peter, prince of the apostles, saying that he himself now sits on it in the persons of his successors. And indeed I acknowledge myself to be unworthy . . . I gladly accepted all that has been said, in that he has spoken to me about Peter’s chair, who occupies Peter’s chair. And, though special honor to myself in no wise delights me . . . who can be ignorant that holy Church has been made firm in the solidity of the prince of the apostles, who derived his name from the firmness of his mind, so as to be called Peter from petra. And to him it is said by the voice of the Truth, ‘To you I will give the keys of the kingdom of heaven’ [Matt. 16:19]. (Letters 40 [A.D. 597]).

Pope Damasus I
"Likewise it is decreed . . . that it ought to be announced that . . . the holy Roman Church has not been placed at the forefront [of the churches] by the conciliar decisions of other churches, but has received the primacy by the evangelic voice of our Lord and Savior, [Matt. 16:18–19]. The first see, therefore, is that of Peter the apostle, that of the Roman Church, which has neither stain nor blemish nor anything like it" (Decree of Damasus 3 [A.D. 382]).

Pope Innocent I
"In seeking the things of God . . . you have acknowledged that judgment is to be referred to us [the pope], and have shown that you know that is owed to the Apostolic See [Rome], if all of us placed in this position are to desire to follow the apostle himself [Peter] from whom the episcopate itself and the total authority of this name have emerged" (Letters 29:1 [A.D. 408]).