Yes. I'm a mathemitician at heart, and so is God. Sometimes His doctrine is written in what we call analytical geometry. If A=B, and B=C, then A=C.
Yes, If A=B and B=C then A=C, but that is not what you then demonstrate below.
In this case with Justification A and Faith Alone B: If A =B, then if B changes, then so must A, or A and B are no longer the same.
If A (justification) is only equal to B (faith alone), then if B changes (faith with works), B is not longer equal to A at all.
The conditional statement should be:
If justification (A) is by faith alone (B), and faith alone (B) is . . . what? You didn't even give a 'C' condition. Your argument is incomplete, not to mention that you haven't defined "justification" yet.
What does the Bible say? Here is some of it:
Rom 3:20 For
by works of the law no human being will be justified in his sight, since through the law comes knowledge of sin.
Rom 3:21 But now the righteousness of God has been manifested apart from the law, although the Law and the Prophets bear witness to it—
Rom 3:22
the righteousness of God through faith in Jesus Christ for all who believe. For there is no distinction:
Rom 3:23 for all have sinned and fall short of the glory of God,
Rom 3:24
and are justified by his grace as a gift, through the redemption that is in Christ Jesus,
Rom 3:25 whom God put forward as a propitiation by his blood,
to be received by faith. This was to show God's righteousness, because in his divine forbearance he had passed over former sins.
Rom 3:26 It was to show his righteousness at the present time, so
that he might be just and the justifier of the one who has faith in Jesus.
Rom 3:27 Then what becomes of our boasting? It is excluded. By what kind of law? By a law of works? No,
but by the law of faith.
Rom 3:28
For we hold that one is justified by faith apart from works of the law.
Rom 3:29 Or is God the God of Jews only? Is he not the God of Gentiles also? Yes, of Gentiles also,
Rom 3:30 since God is one—
who will justify the circumcised by faith and the uncircumcised through faith. (ESV)
Rom 6:23 For the wages of sin is death, but
the free gift of God is eternal life in Christ Jesus our Lord. (ESV)
Rom 10:8 But what does it say? “The word is near you, in your mouth and in your heart” (that is,
the word of faith that we proclaim);
Rom 10:9 because,
if you confess with your mouth that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved.
Rom 10:10
For with the heart one believes and is justified, and with the mouth one confesses and is saved. (ESV)
Gal 2:16 yet
we know that a person is not justified by works of the law but through faith in Jesus Christ, so we also have believed in Christ Jesus,
in order to be justified by faith in Christ and not by works of the law, because by works of the law no one will be justified. (ESV)
Gal 3:1 O foolish Galatians! Who has bewitched you? It was before your eyes that Jesus Christ was publicly portrayed as crucified.
Gal 3:2 Let me ask you only this:
Did you receive the Spirit by works of the law or by hearing with faith?
Gal 3:3
Are you so foolish? Having begun by the Spirit, are you now being perfected by the flesh?
Gal 3:4 Did you suffer so many things in vain—if indeed it was in vain?
Gal 3:5 Does he who supplies the Spirit to you and works miracles among you
do so by works of the law, or by hearing with faith—
Gal 3:6 just as Abraham “believed God, and it was counted to him as righteousness”?
Gal 3:7
Know then that it is those of faith who are the sons of Abraham.
Gal 3:8 And
the Scripture, foreseeing that God would justify the Gentiles by faith, preached the gospel beforehand to Abraham, saying, “In you shall all the nations be blessed.”
Gal 3:9
So then, those who are of faith are blessed along with Abraham, the man of faith.
Gal 3:10
For all who rely on works of the law are under a curse; for it is written, “Cursed be everyone who does not abide by all things written in the Book of the Law, and do them.”
Gal 3:11
Now it is evident that no one is justified before God by the law, for “The righteous shall live by faith.”
Gal 3:12 But
the law is not of faith, rather “The one who does them shall live by them.”
Gal 3:13 Christ redeemed us from the curse of the law by becoming a curse for us—for it is written, “Cursed is everyone who is hanged on a tree”—
Gal 3:14
so that in Christ Jesus the blessing of Abraham might come to the Gentiles, so that we might receive the promised Spirit through faith.
…
Gal 3:21 Is the law then contrary to the promises of God? Certainly not!
For if a law had been given that could give life, then righteousness would indeed be by the law.
Gal 3:22 But the Scripture imprisoned everything under sin,
so that the promise by faith in Jesus Christ might be given to those who believe.
Gal 3:23 Now
before faith came, we were held captive under the law, imprisoned until the coming faith would be revealed.
Gal 3:24 So then, the law was our guardian until Christ came,
in order that we might be justified by faith.
Gal 3:25 But
now that faith has come, we are no longer under a guardian,
Gal 3:26 for
in Christ Jesus you are all sons of God, through faith. (ESV)
Eph 2:4 But God, being rich in mercy, because of the great love with which he loved us,
Eph 2:5 even
when we were dead in our trespasses, made us alive together with Christ—
by grace you have been saved—
Eph 2:6 and raised us up with him and seated us with him in the heavenly places in Christ Jesus,
Eph 2:7 so that in the coming ages he might show the immeasurable riches of his grace in kindness toward us in Christ Jesus.
Eph 2:8
For by grace you have been saved through faith. And this is not your own doing; it is the gift of God,
Eph 2:9
not a result of works, so that no one may boast.
Eph 2:10 For we are his workmanship, created in Christ Jesus
for good works, which God prepared beforehand, that we should walk in them. (ESV)
Tit 3:4 But when the goodness and loving kindness of God our Savior appeared,
Tit 3:5 he saved us,
not because of works done by us in righteousness,
but according to his own mercy, by the washing of regeneration and renewal of the Holy Spirit,
Tit 3:6 whom he poured out on us richly through Jesus Christ our Savior,
Tit 3:7 so that
being justified by his grace we might become heirs according to the hope of eternal life.
Tit 3:8 The saying is trustworthy, and I want you to insist on these things, so that
those who have believed in God may be careful to devote themselves to good works. These things are excellent and profitable for people. (ESV)
The Bible could not be more clear that we are justified (declared righteous by God) by faith alone; neither by works of the law nor works of righteousness. Any who teach otherwise teach another gospel and Paul says they are to be considered accursed (Gal 1:8). Works are to be done in obedience to Christ and as such are
evidence of faith; they
never justify, in the sense of being declared righteous by God.