Theorem nfnf1 1481

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 1395	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1479	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1408	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1287   F/wnf 1394

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-ial 1472

This theorem depends on definitions:  df-bi 115  df-nf 1395

This theorem is referenced by:  nfimd  1522  nfnt  1591  nfald  1690  equs5or  1758  sbcomxyyz  1894  nfsb4t  1938  nfnfc1  2231  sbcnestgf  2979  dfnfc2  3671  bdsepnft  11733  setindft  11815  strcollnft  11834