Theorem nfnf1 1555

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 1472	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1552	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1485	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1362   F/wnf 1471

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 1458  ax-gen 1460  ax-ial 1545

This theorem depends on definitions:  df-bi 117  df-nf 1472

This theorem is referenced by:  nfimd  1596  nfnt  1667  nfald  1771  equs5or  1841  sbcomxyyz  1988  nfsb4t  2030  nfnfc1  2339  nfabdw  2355  sbcnestgf  3132  dfnfc2  3853  bdsepnft  15379  setindft  15457  strcollnft  15476