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Theorem exsimpl 1723
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 459 . 2  |-  ( (
ph  /\  ps )  ->  ph )
21eximi 1703 1  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 371   E.wex 1660
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679
This theorem depends on definitions:  df-bi 189  df-an 373  df-ex 1661
This theorem is referenced by:  19.40  1725  euexALT  2308  moexex  2338  elex  3091  sbc5  3325  r19.2zb  3888  dmcoss  5111  suppimacnvss  6933  unblem2  7828  kmlem8  8589  isssc  15718  bnj1143  29604  bnj1371  29840  bnj1374  29842  bj-elissetv  31434  atex  32934  pm10.55  36620
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