Theorem nfnf1 1885

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 1604	. 2 |- ( F/ x ph <-> A. x ( ph -> A. x ph ) )
2		nfa1 1883	. 2 |- F/ x A. x ( ph -> A. x ph )
3	1, 2	nfxfr 1632	1 |- F/ x F/ x ph

Syntax hints:   -> wi 4   A.wal 1381   F/wnf 1603

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-12 1840

This theorem depends on definitions:  df-bi 185  df-ex 1600  df-nf 1604

This theorem is referenced by:  nfnt  1886  nfimd  1903  nfald  1937  nfeqf2  2027  nfsb4t  2116  nfnfc1  2608  sbcnestgf  3825  dfnfc2  4252  wl-equsal1t  29969  wl-sb6rft  29972  wl-sb8t  29975  wl-mo2t  29995  wl-mo3t  29996  wl-sb8eut  29997  bj-sbf4  34159