Theorem nfnf1 1436

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 1350	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1434	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1363	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1241   F/wnf 1349

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 1336  ax-gen 1338  ax-ial 1427

This theorem depends on definitions:  df-bi 110  df-nf 1350

This theorem is referenced by:  nfimd  1477  nfnt  1546  nfald  1643  equs5or  1711  sbcomxyyz  1846  nfsb4t  1890  nfnfc1  2181  sbcnestgf  2897  dfnfc2  3598  bdsepnft  10007  setindft  10090  strcollnft  10109