Theorem pm2.73 989

Description: Theorem *2.73 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm2.73	⊢ ((𝜑 → 𝜓) → (((𝜑 ∨ 𝜓) ∨ 𝜒) → (𝜓 ∨ 𝜒)))

Proof of Theorem pm2.73

Step	Hyp	Ref	Expression
1		pm2.621 912	. 2 ⊢ ((𝜑 → 𝜓) → ((𝜑 ∨ 𝜓) → 𝜓))
2	1	orim1d 981	1 ⊢ ((𝜑 → 𝜓) → (((𝜑 ∨ 𝜓) ∨ 𝜒) → (𝜓 ∨ 𝜒)))

This proof depends on syntax axioms:   → wi 4   ∨ wo 861

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862

This theorem is used by: (None)