Theorem pm2.81 806

Description: Theorem *2.81 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.81	⊢ ((𝜓 → (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜓) → ((𝜑 ∨ 𝜒) → (𝜑 ∨ 𝜃))))

Proof of Theorem pm2.81

Step	Hyp	Ref	Expression
1		orim2 784	. 2 ⊢ ((𝜓 → (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ (𝜒 → 𝜃))))
2		pm2.76 803	. 2 ⊢ ((𝜑 ∨ (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜒) → (𝜑 ∨ 𝜃)))
3	1, 2	syl6 33	1 ⊢ ((𝜓 → (𝜒 → 𝜃)) → ((𝜑 ∨ 𝜓) → ((𝜑 ∨ 𝜒) → (𝜑 ∨ 𝜃))))

Syntax hints:   → wi 4   ∨ wo 703

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 704

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)