Theorem nfnf1 2001

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 1676	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1999	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1704	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1450   F/wnf 1675

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950

This theorem depends on definitions:  df-bi 190  df-ex 1672  df-nf 1676

This theorem is referenced by:  nfnt  2002  nfimd  2020  nfald  2053  nfeqf2  2148  nfsb4t  2238  nfnfc1  2615  sbcnestgf  3788  dfnfc2  4208  bj-sbf4  31508  wl-equsal1t  31944  wl-sb6rft  31947  wl-sb8t  31950  wl-mo2tf  31970  wl-eutf  31972  wl-mo2t  31974  wl-mo3t  31975  wl-sb8eut  31976