Theorem nfnf1 1567

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 1484	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1564	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1497	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1371   F/wnf 1483

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1470  ax-gen 1472  ax-ial 1557

This theorem depends on definitions:  df-bi 117  df-nf 1484

This theorem is referenced by:  nfimd  1608  nfnt  1679  nfald  1783  equs5or  1853  sbcomxyyz  2000  nfsb4t  2042  nfnfc1  2351  nfabdw  2367  sbcnestgf  3145  dfnfc2  3868  bdsepnft  15860  setindft  15938  strcollnft  15957