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Theorem exlimdh 1808
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 1543 . 2  |-  F/ x ph
3 exlimdh.2 . . 3  |-  ( ch 
->  A. x ch )
43nfi 1543 . 2  |-  F/ x ch
5 exlimdh.3 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
62, 4, 5exlimd 1807 1  |-  ( ph  ->  ( E. x ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   E.wex 1533
This theorem is referenced by:  exlimexi  27558  eexinst01  27560  eexinst11  27561  ax12-2  28370  a12studyALT  28400  a12study3  28402
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1538  ax-5 1549  ax-17 1608  ax-9 1641  ax-8 1648  ax-6 1707  ax-11 1719
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1534  df-nf 1537
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