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Theorem eximdh 1543
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 1399 . 2  |-  ( ph  ->  A. x ( ps 
->  ch ) )
4 exim 1531 . 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 1283   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  eximd  1544  19.41h  1616  hbexd  1625  equsex  1657  equsexd  1658  spimeh  1668  sbiedh  1711  exdistrfor  1722  eximdv  1802  cbvexdh  1843  mopick2  2025  2euex  2029  bj-sbimedh  10718
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