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Theorem exsimpl 1505
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 (x(φ ψ) → xφ)

Proof of Theorem exsimpl
StepHypRef Expression
1 simpl 102 . 2 ((φ ψ) → φ)
21eximi 1488 1 (x(φ ψ) → xφ)
Colors of variables: wff set class
Syntax hints:  wi 4   wa 97  wex 1378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-ial 1424
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  19.40  1519  euex  1927  moexexdc  1981  elex  2560  sbc5  2781  dmcoss  4544  fmptco  5273  brabvv  5493  brtpos2  5807
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