Paul reminds the brothers to "hold firmly to the word I preached to you.  Otherwise, you have believed in vain."

The word Paul spoke to them was salvation through Jesus alone.  Anything else is believing in vain.  It is of no account.  An example would be honoring Jesus as the bread of life as opposed to honoring food sacrificed to idols.

Speaking of Jesus,
“Then he appeared to James, then to all the apostles, and last of all he appeared to me also, as to one abnormally born.”

This James is thought by most scholars to be the brother of Jesus who at first did not believe that Jesus was the Messiah, but later believed and became a leader of the church in Jerusalem.

Paul says that he was abnormally born. Not many of us have the spiritual birth that Paul did.

The resurrected Jesus appeared to more than 500 of the brothers at one time.  Does this mean Jesus only appeared to Believers after the resurrection?

1 Corinthians 15:22-24
For as in Adam all die, even so in Christ all will be made alive. But each in his own order: Christ the first-fruit, and afterward they who are Christ's at His coming; then is the end, when He delivers the kingdom to God, even the Father; when He makes to cease all rule and all authority and power. 

Quite a bit of time takes place between these verses.  Jesus rises first, which has already taken place. Then when He returns to establish His Millennial Kingdom on earth, those who will be with Him are the martyrs, patriarchs of the past, prophets, apostles, and whomever else Jesus chooses. (John 5:21)These will reign with Him on earth for 1,000 years.  After that when Jesus has destroyed all dominion, authority, and power, He will deliver the kingdom to God the Father, the Ancient of Days. (see Daniel 7:9-14). God will raise all the rest of the dead. (John 5:26-29)

Concerning spiritual bodies…we have a natural body and a spiritual body. It’s hard for us to comprehend how our spiritual bodies will look. Imagine an apple seed. If we plant an apple seed, a seed doesn’t grow – ultimately a large beautiful apple tree with leafy branches, beautiful blossoms, and luscious fruit grows. The final result looks nothing like the seed. Our spiritual bodies will be far more beautiful than a “seed”.

“Death has been swallowed up in victory.”
What a statement this is! Death is not defeat. Believers are victors in death because we will have inherited eternal life.

“…because a great door for effective work has been opened to me, and there are many who oppose me.”
Just as Paul did, we may have opposition if we are doing effective work for the Lord. Has a great door been opened to us Believers for effective work? Do we have the courage to walk through that door, knowing we will be empowered by the Holy Spirit or are we weak because there are many who oppose us?

1 Corinthians 15:58
Therefore, my dear brothers, stand firm. Let nothing move you. Always give yourselves fully to the work of the Lord, because you know that your labor in the Lord is not in vain.

So even if we think we aren't making a difference, God says we are! What encouragement!