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Theorem jao 672
Description: Disjunction of antecedents. Compare Theorem *3.44 of [WhiteheadRussell] p. 113. (Contributed by NM, 5-Apr-1994.) (Proof shortened by Wolf Lammen, 4-Apr-2013.)
Assertion
Ref Expression
jao ((𝜑𝜓) → ((𝜒𝜓) → ((𝜑𝜒) → 𝜓)))

Proof of Theorem jao
StepHypRef Expression
1 pm3.44 635 . 2 (((𝜑𝜓) ∧ (𝜒𝜓)) → ((𝜑𝜒) → 𝜓))
21ex 108 1 ((𝜑𝜓) → ((𝜒𝜓) → ((𝜑𝜒) → 𝜓)))
Colors of variables: wff set class
Syntax hints:  wi 4  wo 629
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  3jao  1196  suctr  4158
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