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Theorem exsimpl 1549
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 107 . 2  |-  ( (
ph  /\  ps )  ->  ph )
21eximi 1532 1  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-ial 1468
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  19.40  1563  euex  1972  moexexdc  2026  elex  2611  sbc5  2839  dmcoss  4629  fmptco  5362  brabvv  5582  brtpos2  5900
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