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Theorem exlimih 1731
Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.)
Hypotheses
Ref Expression
exlimih.1  |-  ( ps 
->  A. x ps )
exlimih.2  |-  ( ph  ->  ps )
Assertion
Ref Expression
exlimih  |-  ( E. x ph  ->  ps )

Proof of Theorem exlimih
StepHypRef Expression
1 exlimih.1 . . 3  |-  ( ps 
->  A. x ps )
2119.23h 1730 . 2  |-  ( A. x ( ph  ->  ps )  <->  ( E. x ph  ->  ps ) )
3 exlimih.2 . 2  |-  ( ph  ->  ps )
42, 3mpgbi 1538 1  |-  ( E. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1529   E.wex 1530
This theorem is referenced by:  ax12olem5  1874  ax10lem2  1879  a16g  1887  ceqsex3OLD  26737  ax12OLD  29178  a12study5rev  29195  a12study10  29209  a12study10n  29210  a12study11  29211  a12study11n  29212
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-11 1717
This theorem depends on definitions:  df-bi 177  df-ex 1531
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