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Theorem nfdv 1773
Description: Apply the definition of not-free in a context. (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfdv.1  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Assertion
Ref Expression
nfdv  |-  ( ph  ->  F/ x ps )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem nfdv
StepHypRef Expression
1 nfdv.1 . . 3  |-  ( ph  ->  ( ps  ->  A. x ps ) )
21alrimiv 1770 . 2  |-  ( ph  ->  A. x ( ps 
->  A. x ps )
)
3 df-nf 1366 . 2  |-  ( F/ x ps  <->  A. x
( ps  ->  A. x ps ) )
42, 3sylibr 141 1  |-  ( ph  ->  F/ x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1257   F/wnf 1365
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-17 1435
This theorem depends on definitions:  df-bi 114  df-nf 1366
This theorem is referenced by: (None)
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