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Theorem exsimpr 1618
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
exsimpr  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )

Proof of Theorem exsimpr
StepHypRef Expression
1 simpr 110 . 2  |-  ( (
ph  /\  ps )  ->  ps )
21eximi 1600 1  |-  ( E. x ( ph  /\  ps )  ->  E. x ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104   E.wex 1492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-ial 1534
This theorem depends on definitions:  df-bi 117
This theorem is referenced by:  cbvexv1  1752  onm  4403  imassrn  4983  eliotaeu  5207  fv3  5540  relelfvdm  5549  nfvres  5550  brtpos2  6254  cc1  7266  omiunct  12447
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