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Theorem exsimpr 1597
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 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)

Proof of Theorem exsimpr
StepHypRef Expression
1 simpr 109 . 2 ((𝜑𝜓) → 𝜓)
21eximi 1579 1 (∃𝑥(𝜑𝜓) → ∃𝑥𝜓)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 103  wex 1468
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-ial 1514
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  onm  4323  imassrn  4892  fv3  5444  relelfvdm  5453  nfvres  5454  brtpos2  6148  cc1  7085  omiunct  11968
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