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Theorem jaoi3 1055
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 853 . 2 ((𝜑 ∨ (¬ 𝜑𝜒)) → 𝜓)
43jaoi2 1054 1 ((𝜑𝜒) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 398  wo 843
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 209  df-an 399  df-or 844
This theorem is referenced by:  2mpo0  7396  bropopvvv  7787  bropfvvvv  7789  ssnn0fi  13356  swrdnd  14018  swrdnnn0nd  14020  swrdnd0  14021  pfxnd0  14052  line2ylem  44745  line2xlem  44747  itsclc0xyqsol  44762
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