Theorem pm2.76 754

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 665	. . 3 ⊢ (𝜑 → (𝜑 ∨ 𝜒))
2	1	a1d 22	. 2 ⊢ (𝜑 → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒)))
3		orim2 735	. 2 ⊢ ((𝜓 → 𝜒) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒)))
4	2, 3	jaoi 668	1 ⊢ ((𝜑 ∨ (𝜓 → 𝜒)) → ((𝜑 ∨ 𝜓) → (𝜑 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 661

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 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  pm2.75  755  pm2.81  757  orimdidc  845  equs5or  1751