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Theorem jaoi3 1056
 Description: Inference separating a disjunct of an antecedent. (Contributed by Alexander van der Vekens, 25-May-2018.)
Hypotheses
Ref Expression
jaoi3.1 (𝜑𝜓)
jaoi3.2 ((¬ 𝜑𝜒) → 𝜓)
Assertion
Ref Expression
jaoi3 ((𝜑𝜒) → 𝜓)

Proof of Theorem jaoi3
StepHypRef Expression
1 jaoi3.1 . . 3 (𝜑𝜓)
2 jaoi3.2 . . 3 ((¬ 𝜑𝜒) → 𝜓)
31, 2jaoi 854 . 2 ((𝜑 ∨ (¬ 𝜑𝜒)) → 𝜓)
43jaoi2 1055 1 ((𝜑𝜒) → 𝜓)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 399   ∨ wo 844 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845 This theorem is referenced by:  2mpo0  7390  bropopvvv  7790  bropfvvvv  7792  ssnn0fi  13402  swrdnd  14063  swrdnnn0nd  14065  swrdnd0  14066  pfxnd0  14097  line2ylem  45530  line2xlem  45532  itsclc0xyqsol  45547
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