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Theorem nfnf1 1523
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 1437 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 nfa1 1521 . 2  |-  F/ x A. x ( ph  ->  A. x ph )
31, 2nfxfr 1450 1  |-  F/ x F/ x ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1329   F/wnf 1436
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ial 1514
This theorem depends on definitions:  df-bi 116  df-nf 1437
This theorem is referenced by:  nfimd  1564  nfnt  1634  nfald  1733  equs5or  1802  sbcomxyyz  1943  nfsb4t  1987  nfnfc1  2282  sbcnestgf  3046  dfnfc2  3749  bdsepnft  13070  setindft  13148  strcollnft  13167
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