St. Cyprian of Carthage claimed that all bishops were the successors of Peter…It is in On the Unity of the Church
The context in St. Cyprian’s Treatises where he says that the bishops have equal power is how the bishops are all equal in relation to
the unity that the Eucharist provides to the Church. The subject context is about the Eucharist and not about teaching authority. Catholics agree that every priest has equal power for confecting the Eucharist and that there is a sacramental unity in the Eucharist. But to equate sacramental unity to doctrinal unity is like trying to equate apples to oranges. Here’s a St. Cyprian quote about Peter’s leadership role in the Church from the same work but in Treatise II:
“Peter also, to whom the Lord commends His sheep to be fed and guarded, on whom He placed and founded the Church…” -
St. Cyprian, Treatise II
Also…
St. Cyprian of Carthage on the Papacy
“Peter also, upon whom by the Lord’s condescension the Church was founded…” -
St. Cyprian, Treatise IX
“…Since Rome from her greatness plainly ought to take precedence of Carthage…” -
St. Cyprian, Epistle 48
“Nevertheless, Peter, upon whom by the same Lord the Church had been built, speaking one for all, and answering with the voice of the Church, says…” -
St. Cyprian, Epistle 54
“After such things as these, moreover, they still dare— a false bishop having been appointed for them by, heretics— to set sail and to bear letters from schismatic and profane persons to** the throne of Peter, and to the chief church whence priestly unity takes its source**; and not to consider that these were the Romans whose faith was praised in the preaching of the apostle, to whom faithlessness could have no access.” -
St. Cyprian, Epistle 54
“…Peter speaks there, on whom the Church was to be built, teaching and showing in the name of the Church…” -
St. Cyprian, Epistle 68
“…and the Church founded by Christ the Lord upon Peter, by a source and principle of unity, is one also.” -
St. Cyprian, Epistle 69
“…For neither did Peter, whom first the Lord chose, and upon whom He built His Church…” -
St. Cyprian, Epistle 70
“For first of all the Lord gave that power to
Peter, upon whom He built the Church, and whence He appointed and showed the source of unity— the power, namely, that whatsoever he loosed on earth should be loosed in heaven.” -
St. Cyprian, Epistle 72
“…Moreover, Peter himself, showing and vindicating the unity…” -
St. Cyprian, Epistle 73