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Theorem exlimd 1803
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 1745 . 2  |-  ( ph  ->  A. x ( ps 
->  ch ) )
4 exlimd.2 . . 3  |-  F/ x ch
5419.23 1797 . 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 1527   E.wex 1528   F/wnf 1531
This theorem is referenced by:  exlimdh  1804  exlimdd  1830  equs5  1936  exists2  2233  ceqsalg  2812  copsex2t  4253  mosubopt  4264  alxfr  4547  fvmptdf  5611  ovmpt2df  5979  ov3  5984  tz7.48-1  6455  ac6c4  8108  fsum2dlem  12233  gsum2d2lem  15224  qusp  25542  stoweidlem27  27776  stoweidlem43  27792  stoweidlem44  27793  stoweidlem54  27803  a12study  29132
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1529  df-nf 1532
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