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Theorem exlimih 2016
Description: Inference associated with 19.23 2013. See exlimiv 1784 for a version with a dv condition requiring fewer axioms. (Contributed by NM, 10-Jan-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 1682 . 2  |-  F/ x ps
3 exlimih.2 . 2  |-  ( ph  ->  ps )
42, 3exlimi 2015 1  |-  ( E. x ph  ->  ps )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1450   E.wex 1671
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-12 1950
This theorem depends on definitions:  df-bi 190  df-ex 1672  df-nf 1676
This theorem is referenced by: (None)
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