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Theorem jaoi3 1049
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 393 . 2 ((𝜑 ∨ (¬ 𝜑𝜒)) → 𝜓)
43jaoi2 1048 1 ((𝜑𝜒) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 382  wa 383
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 197  df-or 384  df-an 385
This theorem is referenced by:  2mpt20  7049  bropopvvv  7425  bropfvvvv  7427  ssnn0fi  12999  swrdnd  13653
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