Theorem nfnf1 1981

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 1668	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1979	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1696	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1442   F/wnf 1667

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-12 1933

This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1664  df-nf 1668

This theorem is referenced by:  nfnt  1982  nfimd  2000  nfald  2034  nfeqf2  2135  nfsb4t  2218  nfnfc1  2595  sbcnestgf  3784  dfnfc2  4216  bj-sbf4  31440  wl-equsal1t  31874  wl-sb6rft  31877  wl-sb8t  31880  wl-mo2tf  31900  wl-eutf  31902  wl-mo2t  31904  wl-mo3t  31905  wl-sb8eut  31906