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Theorem exlimdh 1532
Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 28-Jan-1997.)
Hypotheses
Ref Expression
exlimdh.1  |-  ( ph  ->  A. x ph )
exlimdh.2  |-  ( ch 
->  A. x ch )
exlimdh.3  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
exlimdh  |-  ( ph  ->  ( E. x ps 
->  ch ) )

Proof of Theorem exlimdh
StepHypRef Expression
1 exlimdh.1 . . 3  |-  ( ph  ->  A. x ph )
2 exlimdh.3 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2alrimih 1403 . 2  |-  ( ph  ->  A. x ( ps 
->  ch ) )
4 exlimdh.2 . . 3  |-  ( ch 
->  A. x ch )
5419.23h 1432 . 2  |-  ( A. x ( ps  ->  ch )  <->  ( E. x ps  ->  ch ) )
63, 5sylib 120 1  |-  ( ph  ->  ( E. x ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1287   E.wex 1426
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-5 1381  ax-gen 1383  ax-ie2 1428
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  exlimd  1533  exim  1535  exlimdv  1747  equs5  1757  cbvexdh  1849  exists2  2045
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