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Theorem exlimd 1529
Description: Deduction from Theorem 19.9 of [Margaris] p. 89. (Contributed by Mario Carneiro, 24-Sep-2016.) (Proof rewritten by Jim Kingdon, 18-Jun-2018.)
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
21nfri 1453 . 2  |-  ( ph  ->  A. x ph )
3 exlimd.2 . . 3  |-  F/ x ch
43nfri 1453 . 2  |-  ( ch 
->  A. x ch )
5 exlimd.3 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
62, 4, 5exlimdh 1528 1  |-  ( ph  ->  ( E. x ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   F/wnf 1390   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-5 1377  ax-gen 1379  ax-ie2 1424  ax-4 1441
This theorem depends on definitions:  df-bi 115  df-nf 1391
This theorem is referenced by:  exlimdd  1795  ceqsalg  2638  copsex2t  4036  alxfr  4247  mosubopt  4461  ovmpt2df  5711  ovi3  5716  bj-exlimmp  11013
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