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Theorem exlimd 1834
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 1769 . 2  |-  ( ph  ->  A. x ( ps 
->  ch ) )
4 exlimd.2 . . 3  |-  F/ x ch
5419.23 1828 . 2  |-  ( A. x ( ps  ->  ch )  <->  ( E. x ps  ->  ch ) )
63, 5sylib 188 1  |-  ( ph  ->  ( E. x ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1531   E.wex 1532   F/wnf 1535
This theorem is referenced by:  exlimdh  1835  exlimdd  1861  equs5  1968  exists2  2266  ceqsalg  2846  copsex2t  4290  mosubopt  4301  alxfr  4584  fvmptdf  5649  ovmpt2df  6021  ov3  6026  tz7.48-1  6497  ac6c4  8153  fsum2dlem  12280  gsum2d2lem  15273  stoweidlem27  26924  stoweidlem43  26940  stoweidlem44  26941  stoweidlem54  26951  a12study  28950
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1537  ax-5 1548  ax-17 1607  ax-9 1645  ax-8 1666  ax-6 1720  ax-11 1732
This theorem depends on definitions:  df-bi 177  df-ex 1533  df-nf 1536
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