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Theorem exlimih 1782
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 )
21nfi 1556 . 2  |-  F/ x ps
3 exlimih.2 . 2  |-  ( ph  ->  ps )
42, 3exlimi 1781 1  |-  ( E. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   E.wex 1537
This theorem is referenced by:  equid1  1820  ceqsex3OLD  25892  ax12OLD  27794
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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