Theorem nfnf1 1593

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 1510	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1590	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1523	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1396   F/wnf 1509

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 1496  ax-gen 1498  ax-ial 1583

This theorem depends on definitions:  df-bi 117  df-nf 1510

This theorem is referenced by:  nfimd  1634  nfnt  1704  nfald  1808  equs5or  1878  sbcomxyyz  2025  nfsb4t  2067  nfnfc1  2378  nfabdw  2394  sbcnestgf  3180  dfnfc2  3916  bdsepnft  16603  setindft  16681  strcollnft  16700