John 15:26
ESV - 26 But when the Helper comes, whom I will send to you from the Father, the Spirit of truth, who proceeds from the Father, he will bear witness about me.
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The Holy Spirit testifies that Jesus is the Son of God, the Savior of the souls of mankind, for all who believe in Him. He is a witness for Christ. He gives evidence that the Son is risen from the dead and is set to return for the church at any given moment.
These truths are spiritually discerned, however. Likewise, those who worship (acknowledge) God must worship Him in spirit and in truth.
That's the work of the Holy Spirit. He is the go - between of the believer and the Christ. And Christ is the go -between of the believer and the Father. Jesus testifies of the Father; The Holy Spirit testifies of the Son, of Jesus.
Testifying speaks of providing evidence, not merely giving a testimony. Jesus said 'If you don't believe Me, believe the works that I do.' His miracles was evidence that He was sent by the Father.
Anyone who prays "in the Spirit" (with the help of the Spirit, I don't mean as if you're in a trance), has evidence that Jesus is alive. If you've ever prayed without the help of the Spirit, you'll know the difference if you ever begin to pray with the help of the Spirit (what is called "in the Spirit"). It flows like it's being poured out of you.
That's the best evidence of the Holy Spirit, sent by Jesus. He is Jesus' witness!