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Theorem nfnf1 1757
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 1532 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 nfa1 1756 . 2  |-  F/ x A. x ( ph  ->  A. x ph )
31, 2nfxfr 1557 1  |-  F/ x F/ x ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   F/wnf 1531
This theorem is referenced by:  nfnd  1760  nfald  1775  19.23t  1796  spimt  1914  spimed  1917  nfnfc1  2422  sbcnestgf  3128  dfnfc2  3845
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-nf 1532
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