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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
StepHypRef 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 )
31, 2nfxfr 1696 1  |-  F/ x F/ x ph
Colors of variables: wff setvar class
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
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