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Theorem pm4.78i 846
Description: Implication distributes over disjunction. One direction of Theorem *4.78 of [WhiteheadRussell] p. 121. The converse holds in classical logic. (Contributed by Jim Kingdon, 15-Jan-2018.)
Assertion
Ref Expression
pm4.78i (((𝜑𝜓) ∨ (𝜑𝜒)) → (𝜑 → (𝜓𝜒)))

Proof of Theorem pm4.78i
StepHypRef Expression
1 orc 668 . . 3 (𝜓 → (𝜓𝜒))
21imim2i 12 . 2 ((𝜑𝜓) → (𝜑 → (𝜓𝜒)))
3 olc 667 . . 3 (𝜒 → (𝜓𝜒))
43imim2i 12 . 2 ((𝜑𝜒) → (𝜑 → (𝜓𝜒)))
52, 4jaoi 671 1 (((𝜑𝜓) ∨ (𝜑𝜒)) → (𝜑 → (𝜓𝜒)))
Colors of variables: wff set class
Syntax hints:  wi 4  wo 664
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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