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Theorem exsimpl 1581
Description: Simplification of an existentially quantified conjunction. (Contributed by Rodolfo Medina, 25-Sep-2010.) (Proof shortened by Andrew Salmon, 29-Jun-2011.)
Assertion
Ref Expression
exsimpl  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )

Proof of Theorem exsimpl
StepHypRef Expression
1 simpl 108 . 2  |-  ( (
ph  /\  ps )  ->  ph )
21eximi 1564 1  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103   E.wex 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-4 1472  ax-ial 1499
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  19.40  1595  euex  2007  moexexdc  2061  elex  2671  sbc5  2905  dmcoss  4778  fmptco  5554  brabvv  5785  brtpos2  6116
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