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Theorem pm2.81 758
Description: Theorem *2.81 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.81 ((𝜓 → (𝜒𝜃)) → ((𝜑𝜓) → ((𝜑𝜒) → (𝜑𝜃))))

Proof of Theorem pm2.81
StepHypRef Expression
1 orim2 736 . 2 ((𝜓 → (𝜒𝜃)) → ((𝜑𝜓) → (𝜑 ∨ (𝜒𝜃))))
2 pm2.76 755 . 2 ((𝜑 ∨ (𝜒𝜃)) → ((𝜑𝜒) → (𝜑𝜃)))
31, 2syl6 33 1 ((𝜓 → (𝜒𝜃)) → ((𝜑𝜓) → ((𝜑𝜒) → (𝜑𝜃))))
Colors of variables: wff set class
Syntax hints:  wi 4  wo 662
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 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by: (None)
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