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Theorem nfnf1 1954
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 1664 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 nfa1 1952 . 2  |-  F/ x A. x ( ph  ->  A. x ph )
31, 2nfxfr 1692 1  |-  F/ x F/ x ph
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435   F/wnf 1663
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-12 1905
This theorem depends on definitions:  df-bi 188  df-ex 1660  df-nf 1664
This theorem is referenced by:  nfnt  1955  nfimd  1973  nfald  2007  nfeqf2  2096  nfsb4t  2183  nfnfc1  2587  sbcnestgf  3812  dfnfc2  4234  bj-sbf4  31398  wl-equsal1t  31788  wl-sb6rft  31791  wl-sb8t  31794  wl-mo2tf  31814  wl-eutf  31816  wl-mo2t  31818  wl-mo3t  31819  wl-sb8eut  31820
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