Theorem pm2.76 809

Description: Theorem *2.76 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Revised by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
pm2.76	⊢ ((𝜑 ∨ (𝜓 → 𝜒)) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒)))

Proof of Theorem pm2.76

Step	Hyp	Ref	Expression
1		orc 713	. . 3 ⊢ (𝜑 → (𝜑 ∨ 𝜒))
2	1	a1d 22	. 2 ⊢ (𝜑 → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒)))
3		orim2 790	. 2 ⊢ ((𝜓 → 𝜒) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒)))
4	2, 3	jaoi 717	1 ⊢ ((𝜑 ∨ (𝜓 → 𝜒)) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 709

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 710

This theorem depends on definitions:  df-bi 117

This theorem is referenced by:  pm2.75  810  pm2.81  812  orimdidc  907  equs5or  1844