Theorem nfnf1 1523

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 1437	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1521	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1450	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1329   F/wnf 1436

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 1423  ax-gen 1425  ax-ial 1514

This theorem depends on definitions:  df-bi 116  df-nf 1437

This theorem is referenced by:  nfimd  1564  nfnt  1634  nfald  1733  equs5or  1802  sbcomxyyz  1943  nfsb4t  1987  nfnfc1  2282  sbcnestgf  3046  dfnfc2  3749  bdsepnft  13074  setindft  13152  strcollnft  13171