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Theorem 19.9d 1796
Description: A deduction version of one direction of 19.9 1795. (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 1794 . . 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 1531   F/wnf 1534
This theorem is referenced by:  exdistrf  1924  sbied  1989  sbequi  2012  copsexg  4268  19.9d2rf  23198  19.9d2r  23199  exdistrfNEW7  29482  sbiedNEW7  29515  sbequiNEW7  29553
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-ex 1532  df-nf 1535
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