On the contrary - apostolic succession is dead given the RCC's own admitted history of multiple papal lines all with successors all active at the SAME time and all defrocked by Emperor Sigismund - who declared his OWN council of Cardinals to supercede all existing Papal lines. At that time EVERY Papal line was declared to be "antichrist" by its rival popes!
Don't forget, there's more than the Patriarchate of Rome...so even IF Apostolic succession died in the Roman Church (which btw didn't, as an Orthodox Christian we believe that Rome's Bishops orders are vaild), Christ's promise in Matthew 16:18 & 28:20, where Christ promised the "gates of hell would not prevail against the Church and that he Himself would be with the Apostles until the end of the age, would live on in the Orthodox Church...
(And that is if we ignore the fact that the NT provides no such thing as "apostolic succession")
From Holy Scripture:
No one else dared join them, even though they were highly regarded by the people. Acts 5:13 (Note: this shows that the early Christians had a reverence for them)
We have heard that some went out from us without our authorization and disturbed you, troubling your minds by what they said. Acts 15:24
As they traveled from town to town, they delivered the decisions reached by the apostles and elders in Jerusalem for the people to obey. Acts 16:4
For we are not like many, peddling the word of God, but as from sincerity, but as from God, we speak in Christ in the sight of God. 2 Corinthians 2:17 (Note: this shows that the office they hold is more then self appointed authority).
having been built on the foundation of the apostles and prophets, Christ Jesus Himself being the corner stone Eph. 2:20 (Note: the word founation is used to describe "the apostles and prophets", not just St. Peter)
Keep watch over yourselves and all the flock of which the Holy Spirit has made you overseers. Be shepherds of the church of God, which he bought with his own blood. Acts 20:28 (Note: this is a clear testimony that the Holy Spirit appointed the Twelve to be "oeverseers" and "shepherds of the church")
As you sent me into the world, I have sent them into the world. John 17:18 (Note: the Bible compares the ministry of Jesus to that of the Twelve)
The testimony of the early Church:
Through countryside and city [the apostles] preached, and they appointed their earliest converts, testing them by the Spirit, to be the bishops and deacons of future believers. Nor was this a novelty, for bishops and deacons had been written about a long time earlier. . . . Our apostles knew through our Lord Jesus Christ that there would be strife for the office of bishop. For this reason, therefore, having received perfect foreknowledge, they appointed those who have already been mentioned and afterwards added the further provision that, if they should die, other approved men should succeed to their ministry Clement I Letter to the Corinthians 42:4–5, 44:1–3 A.D. 80
When I had come to Rome, I [visited] Anicetus, whose deacon was Eleutherus. And after Anicetus [died], Soter succeeded, and after him Eleutherus. In each succession and in each city there is a continuance of that which is proclaimed by the law, the prophets, and the Lord Hegesippus Memoirs, cited in Eusebius, Ecclesiastical History 4:22 A.D. 180
It is possible, then, for everyone in every church, who may wish to know the truth, to contemplate the tradition of the apostles which has been made known to us throughout the whole world. And we are in a position to enumerate those who were instituted bishops by the apostles and their successors down to our own times, men who neither knew nor taught anything like what these heretics rave about Irenaeus Against Heresies 3:3:1 A.D. 189
[The apostles] founded churches in every city, from which all the other churches, one after another, derived the tradition of the faith, and the seeds of doctrine, and are every day deriving them, that they may become churches. Indeed, it is on this account only that they will be able to deem themselves apostolic, as being the offspring of apostolic churches. Every sort of thing must necessarily revert to its original for its classification. Therefore the churches, although they are so many and so great, comprise but the one primitive Church, [founded] by the apostles, from which they all [spring]. In this way, all are primitive, and all are apostolic, while they are all proved to be one in unity Tertullian Demurrer Against the Heretics 20 A.D. 200
In XC
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