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Theorem 19.9d 1784
Description: A deduction version of one direction of 19.9 1783. (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 1782 . . 3  |-  ( F/ x ph  ->  ( E. x ph  <->  ph ) )
31, 2syl 15 . 2  |-  ( ps 
->  ( E. x ph  <->  ph ) )
43biimpd 198 1  |-  ( ps 
->  ( E. x ph  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 176   E.wex 1528   F/wnf 1531
This theorem is referenced by:  exdistrf  1911  sbied  1976  sbequi  1999  copsexg  4252
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-ex 1529  df-nf 1532
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