Theorem nfxfrd 1409

Description: A utility lemma to transfer a bound-variable hypothesis builder into a definition. (Contributed by Mario Carneiro, 24-Sep-2016.)

Hypotheses

Ref	Expression
nfbii.1	|- ( ph <-> ps )
nfxfrd.2	|- ( ch -> F/ x ps )

Assertion

Ref	Expression
nfxfrd	|- ( ch -> F/ x ph )

Proof of Theorem nfxfrd

Step	Hyp	Ref	Expression
1		nfxfrd.2	. 2 |- ( ch -> F/ x ps )
2		nfbii.1	. . 3 |- ( ph <-> ps )
3	2	nfbii 1407	. 2 |- ( F/ x ph <-> F/ x ps )
4	1, 3	sylibr 132	1 |- ( ch -> F/ x ph )

Syntax hints:   -> wi 4   <-> wb 103   F/wnf 1394

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383

This theorem depends on definitions:  df-bi 115  df-nf 1395

This theorem is referenced by:  nf3and  1506  nfbid  1525  nfsbxy  1866  nfsbxyt  1867  nfeud  1964  nfmod  1965  nfeqd  2243  nfeld  2244  nfabd  2247  nfned  2349  nfneld  2358  nfraldxy  2410  nfrexdxy  2411  nfraldya  2412  nfrexdya  2413  nfsbc1d  2856  nfsbcd  2859  nfbrd  3888