Since salvation is impossible without faith in Christ, there are two elements of procurement; Faith and Christ. Grace is the source “by” which regeneration is available and faith is the vessel “through” which it is procured; “by grace . . . through faith” and not the invert. It’s not the faith that saves, but the Object of faith—Christ; we must also realize that faith does not originate from self, but “is the gift of God” (Eph 2:8).
Christianity or any other system does not effect salvation, for these can only lead to it and are effects of salvation. It is the same concerning that which is of salvation; holiness, righteousness, justification, etc. which are effects of and not causes for salvation. Faith is not to be in these, but solely in Christ - who solely saves. Only that which attributes faith for salvation in Christ solely, is solely Christian. Any alteration by adding or subtracting from this disqualifies it as Christianity altogether; for “A little leaven leaveneth the whole lump” (1 Cor 5:6; Gal 5:9).
“And be found in Him, not having mine own righteousness, which is of the law, but that which is through the faith of Christ, the righteousness which is of God by faith” (Phil 3:9). Paul makes a distinction between two types of righteousness; Law-righteousness and Faith-righteousness. Law-righteousness bases support in self; it is self-righteous or “mine own righteousness”. Faith-righteousness bases support in God; it is Christ’s righteousness or “righteousness which is of God”.
“But that which is through the faith of Christ”; “Not through that faith which Christ Himself, as man, had and exercised on God, as His God; but that which He is the author and finisher of, and which has Him and His righteousness for its object; not through faith, as the cause of it; for the moving cause of justification is the free grace of God, and the efficient cause is God Himself: and it appears from hence, that faith is not the matter of our justification, nor our righteousness; for faith and righteousness are two distinct things, otherwise righteousness could not be said to be "through" faith. The righteousness of Christ is here meant, and which is the sole matter of justification, and comes to us through faith apprehending, receiving, and embracing it; and which shows, that it must be before faith, or it could not be through it; as water that runs through a bridge must be before and after that bridge through which it runs.” -JG
Man’s righteousness, by Law or any source other than the life of Christ is but “filthy rags” (Isa 64:6). The Law, which was not the life of Christ but “a shadow of good things to come, and not the very image of the things” (Heb 10:1), was not intended to produce righteousness, then “verily righteousness should have been by the law” (Gal 3:21). The Father intended acceptable righteousness, not to originate from man alone but from Another (Gen 3:15).
The overall concept is that we are to “live, and move, and have our being” in Christ (Acts 17:28). This is what Paul meant by “nevertheless I live; yet not I, but Christ liveth in me: and the life which I now live in the flesh (physical body) I live by the faith of the Son of God” (Gal 2:20). This is to be mindful that everything we do, which is of God, is being done not by our essence, but by His (Zec 4:6). Though sin lives in us, we do not live in it but in His atonement. In our godliness we live not by our righteousness, but by His righteousness; for it is Christ only who justifies.