Theorem nfnf1 1558

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 1475	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1555	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1488	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1362   F/wnf 1474

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 1461  ax-gen 1463  ax-ial 1548

This theorem depends on definitions:  df-bi 117  df-nf 1475

This theorem is referenced by:  nfimd  1599  nfnt  1670  nfald  1774  equs5or  1844  sbcomxyyz  1991  nfsb4t  2033  nfnfc1  2342  nfabdw  2358  sbcnestgf  3136  dfnfc2  3858  bdsepnft  15617  setindft  15695  strcollnft  15714