Theorem nfnf1 1544

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 1461	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1541	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1474	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1351   F/wnf 1460

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 1447  ax-gen 1449  ax-ial 1534

This theorem depends on definitions:  df-bi 117  df-nf 1461

This theorem is referenced by:  nfimd  1585  nfnt  1656  nfald  1760  equs5or  1830  sbcomxyyz  1972  nfsb4t  2014  nfnfc1  2322  nfabdw  2338  sbcnestgf  3109  dfnfc2  3828  bdsepnft  14642  setindft  14720  strcollnft  14739