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Theorem exlimexi 28706
Description: Inference similar to Theorem 19.23 of [Margaris] p. 90. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
exlimexi.1  |-  ( ps 
->  A. x ps )
exlimexi.2  |-  ( E. x ph  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
exlimexi  |-  ( E. x ph  ->  ps )

Proof of Theorem exlimexi
StepHypRef Expression
1 hbe1 1748 . . 3  |-  ( E. x ph  ->  A. x E. x ph )
2 exlimexi.1 . . 3  |-  ( ps 
->  A. x ps )
3 exlimexi.2 . . 3  |-  ( E. x ph  ->  ( ph  ->  ps ) )
41, 2, 3exlimdh 1828 . 2  |-  ( E. x ph  ->  ( E. x ph  ->  ps ) )
54pm2.43i 46 1  |-  ( E. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1550   E.wex 1551
This theorem is referenced by:  sb5ALT  28707  exinst  28823
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1668  ax-8 1689  ax-6 1746  ax-11 1763
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555
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