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Theorem exsimpl 1524
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 106 . 2 ((𝜑𝜓) → 𝜑)
21eximi 1507 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜑)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 101  wex 1397
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-4 1416  ax-ial 1443
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  19.40  1538  euex  1946  moexexdc  2000  elex  2583  sbc5  2810  dmcoss  4629  fmptco  5358  brabvv  5579  brtpos2  5897
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