You divert from the fact faith precedes regenerationNo, it does not say faith is freely given in John 20:31, and neither did I. Also, it doesn't say that faith precedes spiritual life in John 20:31, you are assuming that, in spite of so many "others scriptures" that teach contrary to that teaching.
That's why when we read the scriptures we must practice Nehemiah 8:8 with all scriptures!
When I read John 20:31 that I know the sense that I must render the words..."But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name~to mean you might have the knowledge of eternal life~because only men who have the power of God given faith, can come the the knowledge of the truth, such truths as Jesus securing the free gift of eternal life for each one given to him of God.
Regeneration by definition is the impartation of life
The following verses show faith precedes life
John 5:24 (KJV) Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life. John 5:25 Verily, verily, I say unto you, The hour is coming, and now is, when the dead shall hear the voice of the Son of God: and they that hear shall live.
John 20:31 (KJV)
31 But these are written, that ye might believe that Jesus is the Christ, the Son of God; and that believing ye might have life through his name.
John 5:40 (KJV)
40 And ye will not come to me, that ye might have life.
Acts 11:18 (KJV)
18 When they heard these things, they held their peace, and glorified God, saying, Then hath God also to the Gentiles granted repentance unto life.
John 6:57 (KJV)
57 As the living Father hath sent me, and I live by the Father: so he that eateth me, even he shall live by me.
Regeneration makes one a child of God. Born of God -
One is made a child of God through faith
John 1:12 (KJV)
12 But as many as received him, to them gave he power to become the sons of God, even to them that believe on his name:
Galatians 3:26 (KJV)
26 For ye are all the children of God by faith in Christ Jesus.
John 12:36 (KJV)
36 While ye have light, believe in the light, that ye may be the children of light. These things spake Jesus, and departed, and did hide himself from them.
Regeneration is a spiritual resurrection.
We are raised spiritually through faith
Colossians 2:12 (KJV)
12 Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead.
One is born again(regenerated) through faith in gospel
James 1:18 (KJV)
18 Of his own will begat he us with the word of truth, that we should be a kind of firstfruits of his creatures.
1 Peter 1:23 (KJV)
23 Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever.
1 Corinthians 4:15 (KJV)
15 For though ye have ten thousand instructors in Christ, yet have ye not many fathers: for in Christ Jesus I have begotten you through the gospel.
Regeneration is the mechanism of salvation
Titus 3:5 (KJV)
5 Not by works of righteousness which we have done, but according to his mercy he saved us, by the washing of regeneration, and renewing of the Holy Ghost;
Ephesians 2:5 (KJV)
5 Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved
it is through faith we are saved
EPH 2:8 (KJV)
Ephesians 2:8 For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:
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Regeneration is preceded by remission of sin
Colossians 2:13 (KJV)
13 And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses;
which requires both faith and repentance
Acts 10:43 (KJV)
43 To him give all the prophets witness, that through his name whosoever believeth in him shall receive remission of sins.
Luke 24:47 (KJV)
47 And that repentance and remission of sins should be preached in his name among all nations, beginning at Jerusalem.
Acts 5:31 (KJV)
31 Him hath God exalted with his right hand to be a Prince and a Saviour, for to give repentance to Israel, and forgiveness of sins.