Peter and Paul in the Roman witness
Irenaeus appeals to the church at Rome as founded and organized by Peter and Paul, then gives a succession list from Linus. This is his late second-century anti-Gnostic argument, not a list of every individual who consecrated the next bishop.
Primary sources
Irenaeus describes:
Irenaeus directly associates the ancient Roman church with the apostles Peter and Paul in his public-tradition argument.
the very ancient, and universally known Church founded and organized at Rome by the two most glorious apostles, Peter and Paul
Passage context and translation
Irenaeus invokes Rome's public apostolic tradition against teachers who claimed secret doctrine. The sentence is an ancient testimony to Peter and Paul's association with Rome; it does not by itself define every later claim about Roman jurisdiction.
Before the excerpt
by indicating that tradition derived from the apostles, of the very great,
After the excerpt
as also [by pointing out] the faith preached to men, which comes down to our time by means of the successions of the bishops