Theorem pm2.74 972

Description: Theorem *2.74 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Andrew Salmon, 7-May-2011.)

Assertion

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

Proof of Theorem pm2.74

Step	Hyp	Ref	Expression
1		orel2 888	. . 3 ⊢ (¬ 𝜓 → ((𝜑 ∨ 𝜓) → 𝜑))
2		ax-1 6	. . 3 ⊢ (𝜑 → ((𝜑 ∨ 𝜓) → 𝜑))
3	1, 2	ja 186	. 2 ⊢ ((𝜓 → 𝜑) → ((𝜑 ∨ 𝜓) → 𝜑))
4	3	orim1d 963	1 ⊢ ((𝜓 → 𝜑) → (((𝜑 ∨ 𝜓) ∨ 𝜒) → (𝜑 ∨ 𝜒)))

Syntax hints:   → wi 4   ∨ wo 844

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845

This theorem is referenced by: (None)