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Theorem exlimih 1812
Description: Inference from Theorem 19.23 of [Margaris] p. 90. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 1-Jan-2018.)
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 1557 . 2  |-  F/ x ps
3 exlimih.2 . 2  |-  ( ph  ->  ps )
42, 3exlimi 1811 1  |-  ( E. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1546   E.wex 1547
This theorem is referenced by:  ax12olem5OLD  1974  ax10lem2OLD  1988  a16gOLD  1998  ceqsex3OLD  26402  a16gNEW7  28884
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-11 1753
This theorem depends on definitions:  df-bi 178  df-ex 1548  df-nf 1551
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