17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith.
For therein — refers back to the gospel mentioned in verse 16, the revelation of the righteousness of God. Righteousness is God’s holiness toward us. Jesus Christ is God’s righteousness. He is how God treats us.
Revealed — continuous, is being revealed
The phrase the faith of Christ is used seven times in Paul’s epistles. In these seven passages faith is spoken of, not objectively, but subjectively.
Objectively, faith is simply trust in another, or in what another has said or done. But subjectively faith is the character which constitutes one worthy of trust. Objectively faith is associated with what one does; subjectively it concerns what he is. One might say, “If I have faith in you, you had better keep faith with me.” Any English dictionary will give these two definitions of the word “faith,” and the same is true of the Greek equivalent, pistis.
In Romans 3:22, Galatians 2:16, Galatians 3:22 and Philippians 3:9 we find “the faith of Christ” and the believer’s faith in Christ mentioned in the same verses, showing the one as complementary to the other.
His trustworthiness is revealed as an appeal to our trust. This interpretation does fit logically with the words that precede and follow. Paul’s gospel reveals the righteousness of God “from faith to faith, as it is written, The just shall live by faith,” i.e. on the principle of faith, faith in the One who always keeps faith with us. — Stam.
I’ve heard this phrase explained as believers passing on the truth to others, and of faith being exercised from dispensation to dispensation. Of all the explanations I read, Stam’s (above) is the one that makes the most sense to me in context.