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Theorem exlimdh 2018
Description: Deduction form of Theorem 19.9 of [Margaris] p. 89. (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 )
21nfi 1682 . 2  |-  F/ x ph
3 exlimdh.2 . . 3  |-  ( ch 
->  A. x ch )
43nfi 1682 . 2  |-  F/ x ch
5 exlimdh.3 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
62, 4, 5exlimd 2017 1  |-  ( ph  ->  ( E. x ps 
->  ch ) )
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:  exlimexi  36951  eexinst01  36953  eexinst11  36954
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