Theorem nfxfrd 1361

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/xps)

Assertion

Ref	Expression
nfxfrd	|- (ch -> F/xph)

Proof of Theorem nfxfrd

Step	Hyp	Ref	Expression
1		nfxfrd.2	. 2 |- (ch -> F/xps)
2		nfbii.1	. . 3 |- (ph <-> ps)
3	2	nfbii 1359	. 2 |- ( F/xph <-> F/xps)
4	1, 3	sylibr 137	1 |- (ch -> F/xph)

Syntax hints:   -> wi 4   <-> wb 98   F/wnf 1346

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335

This theorem depends on definitions:  df-bi 110  df-nf 1347

This theorem is referenced by:  nf3and  1458  nfbid  1477  nfsbxy  1815  nfsbxyt  1816  nfeud  1913  nfmod  1914  nfeqd  2189  nfeld  2190  nfabd  2193  nfned  2292  nfneld  2299  nfraldxy  2350  nfrexdxy  2351  nfraldya  2352  nfrexdya  2353  nfsbc1d  2774  nfsbcd  2777  nfbrd  3798