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Theorem 19.9d 1797
Description: A deduction version of one direction of 19.9 1798. (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 16 . 2  |-  ( ps 
->  ( E. x ph  <->  ph ) )
43biimpd 200 1  |-  ( ps 
->  ( E. x ph  ->  ph ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 178   E.wex 1551   F/wnf 1554
This theorem is referenced by:  exdistrf  2067  exdistrfOLD  2068  sbequi  2112  sbequiOLD  2116  sbiedOLD  2153  copsexg  4444  19.9d2rf  23970  wl-exeq  26236  exdistrfNEW7  29507  sbiedNEW7  29542  sbequiNEW7  29581
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555
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