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Theorem exsimpl 1617
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(𝜑𝜓) → ∃𝑥𝜑)

Proof of Theorem exsimpl
StepHypRef Expression
1 simpl 109 . 2 ((𝜑𝜓) → 𝜑)
21eximi 1600 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  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:  19.40  1631  euex  2056  moexexdc  2110  elex  2750  sbc5  2988  dmcoss  4898  fmptco  5684  brabvv  5923  brtpos2  6254
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