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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
StepHypRef 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 )
31, 2nfxfr 1704 1  |-  F/ x F/ x ph
Colors of variables: wff setvar class
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
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