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Theorem bj-nexdh 33311
Description: Closed form of nexdh 1651 (and more general since it uses  ch). (Contributed by BJ, 6-May-2019.)
Assertion
Ref Expression
bj-nexdh  |-  ( A. x ( ph  ->  -. 
ps )  ->  (
( ch  ->  A. x ph )  ->  ( ch 
->  -.  E. x ps ) ) )

Proof of Theorem bj-nexdh
StepHypRef Expression
1 bj-alrimh 33305 . 2  |-  ( A. x ( ph  ->  -. 
ps )  ->  (
( ch  ->  A. x ph )  ->  ( ch 
->  A. x  -.  ps ) ) )
2 alnex 1598 . 2  |-  ( A. x  -.  ps  <->  -.  E. x ps )
31, 2syl8ib 231 1  |-  ( A. x ( ph  ->  -. 
ps )  ->  (
( ch  ->  A. x ph )  ->  ( ch 
->  -.  E. x ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1377   E.wex 1596
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-4 1612
This theorem depends on definitions:  df-bi 185  df-ex 1597
This theorem is referenced by:  bj-nexdh2  33312  bj-nexdt  33341
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