Theorem nfcxfrd 2763

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 2761	. 2 |- ( F/_ x A <-> F/_ x B )
4	1, 3	sylibr 224	1 |- ( ph -> F/_ x A )

Syntax hints:   -> wi 4   = wceq 1483   F/_wnfc 2751

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-12 2047  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-cleq 2615  df-clel 2618  df-nfc 2753

This theorem is referenced by:  nfcsb1d  3547  nfcsbd  3550  nfifd  4114  nfunid  4443  nfiotad  5854  nfriotad  6619  nfovd  6675  nfnegd  10276  nfxnegd  39668  nfintd  42420  nfiund  42421