To answer your good question, let’s read 2 Corinthians 13:3-5, “Since ye seek a proof of Christ speaking in me, which to you-ward is not weak, but is mighty in you. For though he was crucified through weakness, yet he liveth by the power of God. For we also are weak in him, but we shall live with him by the power of God toward you. Examine yourselves, whether ye be in the faith; prove your own selves. Know ye not your own selves, how that Jesus Christ is in you, except ye be reprobates?”

The Apostle Paul’s role as a servant of God and an apostle was questioned by some of the Corinthians.  They sought “proof of Christ speaking” in Paul.  Certainly, the witness of Paul’s salvation was not weak, in fact, it was ‘mighty’.  So, he directs them to self-examination, to look within themselves, to try, prove, and recognize the condition of their own souls.  If things were right in their relationship with the Lord, they would find a proof of Christ’s speaking in him to them.  So, he advises them to examine the state of their own souls and see whether they were in the faith. 

Rather than them seeking a proof of Christ speaking in Paul, they were exhorted to seek proof of Christ dwelling in them.  William MacDonald in his book, Believer’s Bible Commentary said, “They themselves were the proof of his apostleship.  It was through him that they were led to the Savior.  If they wanted to see his credentials, they should look at themselves.  Paul is not telling the Corinthians to engage in self-examination as a proof of their salvation.  Rather he is asking them to find in their salvation a proof of his apostleship.”  (391.2)