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Theorem nfnf1 1508
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 1422 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 nfa1 1506 . 2  |-  F/ x A. x ( ph  ->  A. x ph )
31, 2nfxfr 1435 1  |-  F/ x F/ x ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1314   F/wnf 1421
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 1408  ax-gen 1410  ax-ial 1499
This theorem depends on definitions:  df-bi 116  df-nf 1422
This theorem is referenced by:  nfimd  1549  nfnt  1619  nfald  1718  equs5or  1786  sbcomxyyz  1923  nfsb4t  1967  nfnfc1  2261  sbcnestgf  3021  dfnfc2  3724  bdsepnft  13012  setindft  13090  strcollnft  13109
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