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Theorem exlimd 1784
Description: Deduction from Theorem 19.23 of [Margaris] p. 90. (Contributed by Mario Carneiro, 24-Sep-2016.)
Hypotheses
Ref Expression
exlimd.1  |-  F/ x ph
exlimd.2  |-  F/ x ch
exlimd.3  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
exlimd  |-  ( ph  ->  ( E. x ps 
->  ch ) )

Proof of Theorem exlimd
StepHypRef Expression
1 exlimd.1 . . 3  |-  F/ x ph
2 exlimd.3 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2alrimi 1706 . 2  |-  ( ph  ->  A. x ( ps 
->  ch ) )
4 exlimd.2 . . 3  |-  F/ x ch
5419.23 1777 . 2  |-  ( A. x ( ps  ->  ch )  <->  ( E. x ps  ->  ch ) )
63, 5sylib 190 1  |-  ( ph  ->  ( E. x ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6   A.wal 1532   E.wex 1537   F/wnf 1539
This theorem is referenced by:  exlimdh  1785  exlimdv  1932  exlimdd  1933  equs5  1943  exists2  2203  ceqsalg  2750  copsex2t  4146  mosubopt  4157  alxfr  4438  fvmptdf  5463  ovmpt2df  5831  ov3  5836  tz7.48-1  6341  ac6c4  7992  fsum2dlem  12110  gsum2d2lem  15059  qusp  24708  a12study  27821
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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