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Theorem bj-nfdt0 30799
Description: A theorem close to a closed form of nfd 1902 and nfdh 1903. (Contributed by BJ, 2-May-2019.)
Assertion
Ref Expression
bj-nfdt0  |-  ( A. x ( ph  ->  ( ps  ->  A. x ps ) )  ->  ( A. x ph  ->  F/ x ps ) )

Proof of Theorem bj-nfdt0
StepHypRef Expression
1 alim 1653 . 2  |-  ( A. x ( ph  ->  ( ps  ->  A. x ps ) )  ->  ( A. x ph  ->  A. x
( ps  ->  A. x ps ) ) )
2 df-nf 1638 . 2  |-  ( F/ x ps  <->  A. x
( ps  ->  A. x ps ) )
31, 2syl6ibr 227 1  |-  ( A. x ( ph  ->  ( ps  ->  A. x ps ) )  ->  ( A. x ph  ->  F/ x ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1403   F/wnf 1637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 1652
This theorem depends on definitions:  df-bi 185  df-nf 1638
This theorem is referenced by:  bj-nfdt  30800
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