The term "apostolic succession" refers to the line of bishops stretching back to the apostles. It is also linked to the validity of most sacraments, making it a very important issue. (More info below.)
"Leaders" were clearly important in the NT, as evidenced by what Paul writes in Hebrews 13:17...
"Obey your leaders and submit to them, for they keep watch over your souls as those who will give an account."
Now, how does one become a "leader"? Does one become a leader through apostolic succession, or does one become a leader whenever they want to go off and start their own little church down the street?
Christ had at least two important things to say to the apostles on the matter.
Luke 22:28-30 (NASB) - "You are those who have stood by Me in My trials; and just as My Father has granted Me a kingdom, I grant you that you may eat and drink at My table in My kingdom, and you will sit on thrones judging the twelve tribes of Israel."
John 20:23 (NASB) - "If you forgive the sins of any, their sins have been forgiven them; if you retain the sins of any, they have been retained."
From those two passages, we can gather that the apostles were given special authority.
2 Timothy 2:2 (NASB) - "The things which you have heard from me in the presence of many witnesses, entrust these to faithful men who will be able to teach others also."
In that verse, Paul refers to the first three generations of apostolic succession—his own generation, Timothy's generation, and the generation Timothy will teach. This clearly indicates that authority gets passed on.
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