Theorem nfnf1 1554

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 1471	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1551	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1484	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1361   F/wnf 1470

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 1457  ax-gen 1459  ax-ial 1544

This theorem depends on definitions:  df-bi 117  df-nf 1471

This theorem is referenced by:  nfimd  1595  nfnt  1666  nfald  1770  equs5or  1840  sbcomxyyz  1982  nfsb4t  2024  nfnfc1  2332  nfabdw  2348  sbcnestgf  3120  dfnfc2  3839  bdsepnft  14935  setindft  15013  strcollnft  15032