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Theorem 19.9d 1551
Description: A deduction version of one direction of 19.9 1535. (Contributed by NM, 5-Aug-1993.) (Revised by Mario Carneiro, 24-Sep-2016.)
Hypothesis
Ref Expression
19.9d.1  |-  ( ps 
->  F/ x ph )
Assertion
Ref Expression
19.9d  |-  ( ps 
->  ( E. x ph  ->  ph ) )

Proof of Theorem 19.9d
StepHypRef Expression
1 19.9d.1 . . 3  |-  ( ps 
->  F/ x ph )
2 19.9t 1533 . . 3  |-  ( F/ x ph  ->  ( E. x ph  <->  ph ) )
31, 2syl 14 . 2  |-  ( ps 
->  ( E. x ph  <->  ph ) )
43biimpd 132 1  |-  ( ps 
->  ( E. x ph  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98   F/wnf 1349   E.wex 1381
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400
This theorem depends on definitions:  df-bi 110  df-nf 1350
This theorem is referenced by: (None)
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