Theorem nfnf1 1524

Description: x is not free in F/ x ph. (Contributed by Mario Carneiro, 11-Aug-2016.)

Assertion

Ref	Expression
nfnf1	|- F/ x F/ x ph

Proof of Theorem nfnf1

Step	Hyp	Ref	Expression
1		df-nf 1438	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1522	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1451	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1330   F/wnf 1437

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ial 1515

This theorem depends on definitions:  df-bi 116  df-nf 1438

This theorem is referenced by:  nfimd  1565  nfnt  1635  nfald  1734  equs5or  1803  sbcomxyyz  1946  nfsb4t  1990  nfnfc1  2285  sbcnestgf  3056  dfnfc2  3762  bdsepnft  13256  setindft  13334  strcollnft  13353