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Theorem eximdh 1681
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 . 2  |-  ( ph  ->  A. x ph )
2 eximdh.2 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32aleximi 1661 . 2  |-  ( A. x ph  ->  ( E. x ps  ->  E. x ch ) )
41, 3syl 16 1  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1397   E.wex 1620
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639
This theorem depends on definitions:  df-bi 185  df-ex 1621
This theorem is referenced by:  eximdv  1718  eximd  1890  ax6e2eq  33670
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