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Theorem nfnf1 1885
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 1604 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 nfa1 1883 . 2  |-  F/ x A. x ( ph  ->  A. x ph )
31, 2nfxfr 1632 1  |-  F/ x F/ x ph
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1381   F/wnf 1603
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1605  ax-4 1618  ax-5 1691  ax-6 1734  ax-7 1776  ax-10 1823  ax-12 1840
This theorem depends on definitions:  df-bi 185  df-ex 1600  df-nf 1604
This theorem is referenced by:  nfnt  1886  nfimd  1903  nfald  1937  nfeqf2  2027  nfsb4t  2116  nfnfc1  2608  sbcnestgf  3825  dfnfc2  4252  wl-equsal1t  29969  wl-sb6rft  29972  wl-sb8t  29975  wl-mo2t  29995  wl-mo3t  29996  wl-sb8eut  29997  bj-sbf4  34159
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