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Theorem exsimpl 1698
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 455 . 2  |-  ( (
ph  /\  ps )  ->  ph )
21eximi 1677 1  |-  ( E. x ( ph  /\  ps )  ->  E. x ph )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 367   E.wex 1633
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652
This theorem depends on definitions:  df-bi 185  df-an 369  df-ex 1634
This theorem is referenced by:  19.40  1700  euexALT  2283  moexex  2314  elex  3067  sbc5  3301  r19.2zb  3862  dmcoss  5082  suppimacnvss  6911  unblem2  7806  kmlem8  8568  isssc  15431  bnj1143  29163  bnj1371  29399  bnj1374  29401  bj-elissetv  30988  atex  32403  pm10.55  36102
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