Greek Father, holy Irenaeus (130-202 AD), bishop of Lugdunum Gaul (modern day Lyons, France) spoke of the distinctive trustworthiness of the doctrine which was taught at the Roman Church for reasons of its apostolicity and its superior origin. Many have severely downplayed St. Irenaeus as a witness to the early Papacy because his descriptions are more accidental than institutional. Rome just happened to be the geographic point where Sts Paul and Peter preached, taught, and died, and that both seem to be equally the foundation of this church.
I’ve provided a link (see bottom) to a thorough study on St. Ireneaus and the Roman Primacy for your pleasure. All I will say in response to the issue raised in the above paragraph is that even if it were the case that St. Irenaeus only spoke in terms which show Rome as superior by accident, rather than with the hint of a specific institution of Papal office, this does not mean he disbelieved in that institution. But more importantly, what gets missed in all of this is that the Greek bishop is *holding Rome as a the pre-eminent example of orthodox and apostolic tradition*, and thus one should take note. This is fundamentally supportive for the early Papacy since St. Irenaeus writes around 180 AD. I will expand.
It was around the same time of St. Irenaeus that Pope St. Victor took action to ensure uniformity of the discipline of celebrating Pascha, and to such a degree that he attempted to bind churches far outside the jurisdiction of the Roman church far to the East in Asia. While it is true no Papal prerogative was written down to survive our day, but surely these actions indicate that the bishop of Rome was looking outside to ensure both uniformity and conformity to its own practice, whether verified by synodal procedure or not. And then, it was only 50 years past St. Irenaeus that Pope Stephen (220?- died 257) did the same as Victor in regard to the question of heretical baptisms. However, by then, Stephen claimed to exercise a rightful oversight over all the churches in order to ensure uniformity and conformity with Roman practice on the basis of his unique succession to St. Peter. And we have the survival of this evidence from St. Firmilian of Caesarea. How likely is it that we get the résumé of Rome’s apostolic superiority & trustworthiness from St. Irenaeus who died in 202, and that in 50 years the Roman See becomes entrenched in the “heresy” of Papalmania? I think it is hardly a likely possibility, especially given that Pope Victor acted similarly. It is much more likely that the consciousness of responsibility to ensure the unity of the Churches in Victor was the same as Stephen’s. And concerning Victor, no one at the time, perhaps beside St. Polycrates and the Asiatic bishops, argued against the authority to do as he did, despite their insistence on his abuse of that authority. Up until this day there have been saintly bishops who have been outspoken on the wrong-use of Papal authority. That being said, it is still not surprisingly that the Victorian mandate on the date of Pascha was brought to uniformity at least by the time of NIcaea 325 AD, since at the Council it was held that the Pascha celebration be had on the Lord’s Day of the week, and not the 14th day of Nisan. So while we don’t know how the dispute between Victor and Asia ended up, we see that the Roman tradition won out into the consensus. But even then, it is reported that Christians continued to celebrate Pascha on the 14th day of Nisan up and into the 5th century AD.
Are we surprised then to see the same play out with the Papal act of Pope Stephen? Surely, the belief against re-baptism for those even baptized by heretics (special cases duly noted) won out to be the consensus view of the Church as proven by the writings of St. Jerome, St. Augustine, and St. Vincent of Lerins, the latter being a most quoted expert on the belief of all times, in all places, by all Christians. But, in the time concurrent with Stephen, both St Cyprian and St Firmlian spoke violently of Stephen’s action. I recommend Dom John Chapman’s writings on Cyprian for more details.
In conclusion, I think St. Irenaeus’ words on the Roman primacy do bear witness to the early Papacy, even if they say nothing specifically of Papal/Petrine prerogatives, when it is read in a broader corroboration with nearby historical facts.
Please enjoy Dominic J. Unger O.F.M. Cap and his study on St. Irenaeus and the Papal Primacy- see link below