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Theorem eximdh 1575
Description: Deduction from Theorem 19.22 of [Margaris] p. 90. (Contributed by NM, 20-May-1996.)
Hypotheses
Ref Expression
eximdh.1  |-  ( ph  ->  A. x ph )
eximdh.2  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
eximdh  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)

Proof of Theorem eximdh
StepHypRef Expression
1 eximdh.1 . . 3  |-  ( ph  ->  A. x ph )
2 eximdh.2 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2alrimih 1552 . 2  |-  ( ph  ->  A. x ( ps 
->  ch ) )
4 exim 1562 . 2  |-  ( A. x ( ps  ->  ch )  ->  ( E. x ps  ->  E. x ch ) )
53, 4syl 15 1  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   E.wex 1528
This theorem is referenced by:  eximdv  1608  eximd  1750  a9e2eq  28323
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544
This theorem depends on definitions:  df-bi 177  df-ex 1529
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