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Theorem eximdh 1591
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 1446 . 2  |-  ( ph  ->  A. x ( ps 
->  ch ) )
4 exim 1579 . 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 1330   E.wex 1469
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-ial 1515
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  eximd  1592  19.41h  1664  hbexd  1673  equsex  1707  equsexd  1708  spimeh  1718  sbiedh  1761  exdistrfor  1773  eximdv  1853  cbvexdh  1899  mopick2  2083  2euex  2087  bj-sbimedh  13147
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