Theorem nfcxfrd 2590

Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by Mario Carneiro, 11-Aug-2016.)

Hypotheses

Ref	Expression
nfceqi.1	|- A = B
nfcxfrd.2	|- ( ph -> F/_ x B )

Assertion

Ref	Expression
nfcxfrd	|- ( ph -> F/_ x A )

Proof of Theorem nfcxfrd

Step	Hyp	Ref	Expression
1		nfcxfrd.2	. 2 |- ( ph -> F/_ x B )
2		nfceqi.1	. . 3 |- A = B
3	2	nfceqi 2588	. 2 |- ( F/_ x A <-> F/_ x B )
4	1, 3	sylibr 216	1 |- ( ph -> F/_ x A )

Syntax hints:   -> wi 4   = wceq 1443   F/_wnfc 2578

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-12 1932  ax-ext 2430

This theorem depends on definitions:  df-bi 189  df-an 373  df-tru 1446  df-ex 1663  df-nf 1667  df-cleq 2443  df-clel 2446  df-nfc 2580

This theorem is referenced by:  nfcsb1d  3376  nfcsbd  3379  nfifd  3908  nfunid  4204  nfiotad  5548  nfriotad  6258  nfovd  6313  nfnegd  9867