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Theorem pm4.78i 801
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 → (ψ χ)))

Proof of Theorem pm4.78i
StepHypRef Expression
1 orc 620 . . 3 (ψ → (ψ χ))
21imim2i 12 . 2 ((φψ) → (φ → (ψ χ)))
3 olc 619 . . 3 (χ → (ψ χ))
43imim2i 12 . 2 ((φχ) → (φ → (ψ χ)))
52, 4jaoi 623 1 (((φψ) (φχ)) → (φ → (ψ χ)))
Colors of variables: wff set class
Syntax hints:  wi 4   wo 616
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 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by: (None)
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