Our Lord whose precepts and warnings we ought to observe, determining the honour of a Bishop and the ordering of His own Church, speaks in the Gospel and says to Peter, I say unto thee, that thou art Peter, and on this rock I will build My Church; and the gates of hell shall not prevail against it. And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven. Thence the ordination of Bishops, and the ordering of the Church, runs down along the course of time and line of succession, so that the Church is settled upon her Bishops; and every act of the Church is regulated by these same Prelates (A Library of the Fathers of the Holy Catholic Church (Oxford: Parker, 1844), The Epistles of S. Cyprian, Ep. 33.1).
Catholic scholar Robert Eno comments, “Cyprian makes considerable use of the image of Peter’s cathedra or chair. Note however that it is important in his theology of the local church: ‘God is one and Christ is one: there is one Church and one chair founded, by the Lord’s authority, upon Peter. It is not possible that another altar can be set up, or that a new priesthood can be appointed, over and above this one altar and this one priesthood’ (Ep. 43.5).
The cathedri Petri symbolism has been the source of much misunderstanding and dispute. Perhaps it can be understood more easily by looking at the special treatise he wrote to defend both his own position as sole lawful bishop of Carthage and that of Cornelius against Novatian, namely, the De unitate ecclesiae, or, as it was known in the Middle Ages, On the Simplicity of Prelates. The chapter of most interest is the fourth. Controversy has dogged this work because two versions of this chapter exist. Since the Reformation, acceptance of one version or the other has usually followed denominational lines.
Much of this has subsided in recent decades especially with the work of Fr. Maurice Bevenot, an English Jesuit, who devoted most of his scholarly life to this text. He championed the suggestion of the English Benedictine, John Chapman, that what we are dealing with here are two versions of a text, both of which were authored by Cyprian. This view has gained wide acceptance in recent decades. Not only did Cyprian write both but his theology of the Church is unchanged from the first to the second. He made textual changes because his earlier version was being misused.
The theology of the controverted passage sees in Peter the symbol of unity, not from his being given greater authority by Christ for, as he says in both versions, ‘…a like power is given to all the Apostles’ and ‘…No doubt the others were all that Peter was.’ Yet Peter was given the power first: ‘Thus it is made clear that there is but one Church and one chair.’ The Chair of Peter then belongs to each lawful bishop in his own see. Cyprian holds the Chair of Peter in Carthage and Cornelius in Rome over against Novatian the would–be usurper. You must hold to this unity if you are to remain in the Church. Cyprian wants unity in the local church around the lawful bishop and unity among the bishops of the world who are ‘glued together’ (Ep. 66.8).
Apart from his good relations and harmony with Bishop Cornelius over the matter of the lapsed, what was Cyprian’s basic view of the role, not of Peter as symbol of unity, but of Rome in the contemporary Church? Given what we have said above, it is clear that he did not see the bishop of Rome as his superior, except by way of honor, even though the lawful bishop of Rome also held the chair of Peter in an historical sense (Ep. 52.2). Another term frequently used by the Africans in speaking of the Church was ‘the root’ (radix). Cyprian sometimes used the term in connection with Rome, leading some to assert that he regarded the Roman church as the ‘root.’ But in fact, in Cyprian’s teaching, the Catholic Church as a whole is the root. So when he bade farewell to some Catholics travelling to Rome, he instructed them to be very careful about which group of Christians they contacted after their arrival in Rome. They must avoid schismatic groups like that of Novation. They should contact and join the Church presided over by Cornelius because it alone is the Catholic Church in Rome. In other words, Cyprian exhorted ‘…them to discern the womb and root…of the Catholic Church and to cleave to it’ (Ep. 48.3).
It is clear that in Cyprian’s mind…one theological conclusion he does not draw is that the bishop of Rome has authority which is superior to that of the African bishops (Robert Eno, The Rise of the Papacy (Wilmington: Michael Glazier, 1990), pp. 57-60).”
Yet, I don’t see any evidence of this beyond your assertion.
Don’t see any evidence of what? That Rome asserts that it was always believed and held? See the canons of Vatican I.