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Theorem eximdh 1621
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 1479 . 2  |-  ( ph  ->  A. x ( ps 
->  ch ) )
4 exim 1609 . 2  |-  ( A. x ( ps  ->  ch )  ->  ( E. x ps  ->  E. x ch ) )
53, 4syl 14 1  |-  ( ph  ->  ( E. x ps 
->  E. x ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1361   E.wex 1502
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-ial 1544
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  eximd  1622  19.41h  1695  hbexd  1704  equsex  1738  equsexd  1739  spimeh  1749  sbiedh  1797  exdistrfor  1810  eximdv  1890  cbvexdh  1936  mopick2  2119  2euex  2123  bj-sbimedh  14819
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