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Theorem exinst 28701
Description: Existential Instantiation. Virtual deduction form of exlimexi 28586. (Contributed by Alan Sare, 21-Apr-2013.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
exinst.1  |-  ( ps 
->  A. x ps )
exinst.2  |-  (. E. x ph ,. ph  ->.  ps ).
Assertion
Ref Expression
exinst  |-  ( E. x ph  ->  ps )

Proof of Theorem exinst
StepHypRef Expression
1 exinst.1 . 2  |-  ( ps 
->  A. x ps )
2 exinst.2 . . 3  |-  (. E. x ph ,. ph  ->.  ps ).
32dfvd2i 28653 . 2  |-  ( E. x ph  ->  ( ph  ->  ps ) )
41, 3exlimexi 28586 1  |-  ( E. x ph  ->  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   E.wex 1531   (.wvd2 28645
This theorem is referenced by:  sb5ALTVD  29005
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535  df-vd2 28646
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