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Theorem exlimexi 28343
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 1707 . . 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 1806 . 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 1529   E.wex 1530
This theorem is referenced by:  sb5ALT  28344  exinst  28458
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-11 1717
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1531  df-nf 1534
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