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Theorem nfnf1 1769
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 1535 . 2  |-  ( F/ x ph  <->  A. x
( ph  ->  A. x ph ) )
2 nfa1 1768 . 2  |-  F/ x A. x ( ph  ->  A. x ph )
31, 2nfxfr 1560 1  |-  F/ x F/ x ph
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   F/wnf 1534
This theorem is referenced by:  nfnd  1772  nfald  1787  19.23t  1808  spimt  1927  spimed  1930  nfnfc1  2435  sbcnestgf  3141  dfnfc2  3861  nfaldwAUX7  29429  spimtNEW7  29484  spimedNEW7  29487  nfaldOLD7  29644
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-nf 1535
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