Theorem nfnf1 1537

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 1454	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1534	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1467	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1346   F/wnf 1453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ial 1527

This theorem depends on definitions:  df-bi 116  df-nf 1454

This theorem is referenced by:  nfimd  1578  nfnt  1649  nfald  1753  equs5or  1823  sbcomxyyz  1965  nfsb4t  2007  nfnfc1  2315  nfabdw  2331  sbcnestgf  3100  dfnfc2  3814  bdsepnft  13922  setindft  14000  strcollnft  14019