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Theorem exlimexi 28287
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 1705 . . 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 1804 . 2  |-  ( E. x ph  ->  ( E. x ph  ->  ps ) )
54pm2.43i 43 1  |-  ( E. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527   E.wex 1528
This theorem is referenced by:  sb5ALT  28288  exinst  28396
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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