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Theorem jaoi2 1082
Description: Inference removing a negated conjunct in a disjunction of an antecedent if this conjunct is part of the disjunction. (Contributed by Alexander van der Vekens, 3-Nov-2017.) (Proof shortened by Wolf Lammen, 21-Sep-2018.)
Hypothesis
Ref Expression
jaoi2.1 ((𝜑 ∨ (¬ 𝜑𝜒)) → 𝜓)
Assertion
Ref Expression
jaoi2 ((𝜑𝜒) → 𝜓)

Proof of Theorem jaoi2
StepHypRef Expression
1 pm5.63 1043 . 2 ((𝜑𝜒) ↔ (𝜑 ∨ (¬ 𝜑𝜒)))
2 jaoi2.1 . 2 ((𝜑 ∨ (¬ 𝜑𝜒)) → 𝜓)
31, 2sylbi 208 1 ((𝜑𝜒) → 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wa 384  wo 873
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 198  df-an 385  df-or 874
This theorem is referenced by:  jaoi3  1083
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