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Theorem exlimd 1807
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 1749 . 2  |-  ( ph  ->  A. x ( ps 
->  ch ) )
4 exlimd.2 . . 3  |-  F/ x ch
5419.23 1801 . 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 1529   E.wex 1530   F/wnf 1533
This theorem is referenced by:  exlimdh  1808  exlimdd  1834  equs5  1941  exists2  2236  ceqsalg  2815  copsex2t  4254  mosubopt  4265  alxfr  4548  fvmptdf  5574  ovmpt2df  5942  ov3  5947  tz7.48-1  6452  ac6c4  8105  fsum2dlem  12229  gsum2d2lem  15220  qusp  24943  stoweidlem27  27177  stoweidlem43  27193  stoweidlem44  27194  stoweidlem54  27204  a12study  28401
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1638  ax-8 1646  ax-6 1706  ax-11 1718
This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1531  df-nf 1534
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