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Theorem exlimdh 1816
Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (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 1541 . 2  |-  F/ x ph
3 exlimdh.2 . . 3  |-  ( ch 
->  A. x ch )
43nfi 1541 . 2  |-  F/ x ch
5 exlimdh.3 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
62, 4, 5exlimd 1815 1  |-  ( ph  ->  ( E. x ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   E.wex 1531
This theorem is referenced by:  exlimexi  28586  eexinst01  28588  eexinst11  28589  equs5NEW7  29509  ax12-2  29725  a12studyALT  29755  a12study3  29757
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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