I write these things to you who believe in the name of the Son of God, that you may know that you have eternal life.
13 These things have I written unto you As there ought to be a daily progress in faith, so he says that he wrote to those who had already believed, so that they might believe more firmly and with greater certainty, and thus enjoy a fuller confidence as to eternal life.
The believer carries inward proof: he has seen his sin and need, beheld Christ's excellency and suitableness to it, felt the power of His word remaking him, and discovered love kindled to God through this revelation. That is testimony no argument can shake.
AI summary
Commenting on 1 John 5:10-13
These things have I written unto you,.... Which are contained in the epistle in general, and particularly what is written in the context, concerning the victory of the world, being ascribed to him who believes that Christ is the Son of God; and concerning the six witnesses of his sonship, and the record bore by God, that the gift of eternal life is in him...