Cyprian also supported the hierarchical tendency which conceived of the Lord's Supper as a sacrificial act, with the bishop offering the sacrifice to God in place of Christ.
The bishop, therefore, stands at the head of the congregation as Christ's representative. Cyprian also believed, in consequence of the foregoing, that each congregation should have but one bishop, inasmuch as this office represents the unity of the church. "There is one man for the time priest in the church, and for the time judge in the stead of Christ" (Epistle 59 [54], 5). He did not mean by this that one bishop could dominate all of the others; he simply meant that each congregation was to be united under a single bishop. The whole of the church of Christ is to be found in each congregation. As it turned out, however, his ideas contributed to the assumption of "primacy" on the part of the bishops of Rome. This claim began to be made in Cyprian's era, and it subsequently resulted in the papal doctrine -- that the pope is the vicar of Christ on earth.
Cyprian looked upon Peter as the symbol of the church's unity (cf. Matt. 16:18). But he also felt that the other apostles possessed the same degree of authority. And in opposing those who asserted the Roman primacy, he referred (among other things) to Gal. 2, where we are told that Paul stood up to Peter and rebuked him.
But one of Cyprian's contemporaries, Bishop Stephen of Rome (254-57), concluded that the bishop of Rome, who was the successor of Peter, the chief apostle, thereby had supremacy over all of the other bishops. He assumed this power for himself and dramatized his claim by demanding obedience from the other bishops and by personally appointing bishops in Gaul and Spain. He claimed "the chair of Peter" on the ground of succession, and he spoke of the "primacy" of the bishop of Rome.
Cyprian and others opposed this claim, but Stephen won out.