Theorem pm2.74 819

Description: Theorem *2.74 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Mario Carneiro, 31-Jan-2015.)

Assertion

Ref	Expression
pm2.74	⊢ ((𝜓 → 𝜑) → (((𝜑 ∨ 𝜓) ∨ 𝜒) → (𝜑 ∨ 𝜒)))

Proof of Theorem pm2.74

Step	Hyp	Ref	Expression
1		idd 21	. . 3 ⊢ ((𝜓 → 𝜑) → (𝜑 → 𝜑))
2		id 19	. . 3 ⊢ ((𝜓 → 𝜑) → (𝜓 → 𝜑))
3	1, 2	jaod 729	. 2 ⊢ ((𝜓 → 𝜑) → ((𝜑 ∨ 𝜓) → 𝜑))
4	3	orim1d 799	1 ⊢ ((𝜓 → 𝜑) → (((𝜑 ∨ 𝜓) ∨ 𝜒) → (𝜑 ∨ 𝜒)))

This proof depends on syntax axioms:   → wi 4   ∨ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by: (None)