Theorem pm2.85

Description: Theorem *2.85 of WhiteheadRussell p. 108. (Contributed by NM, 3-Jan-2005) (Proof shortened by Wolf Lammen, 5-Jan-2013)

	Ref	Expression
Assertion	pm2.85	⊢ ( ( ( 𝜑 ∨ 𝜓 ) → ( 𝜑 ∨ 𝜒 ) ) → ( 𝜑 ∨ ( 𝜓 → 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		orimdi	⊢ ( ( 𝜑 ∨ ( 𝜓 → 𝜒 ) ) ↔ ( ( 𝜑 ∨ 𝜓 ) → ( 𝜑 ∨ 𝜒 ) ) )
2	1	biimpri	⊢ ( ( ( 𝜑 ∨ 𝜓 ) → ( 𝜑 ∨ 𝜒 ) ) → ( 𝜑 ∨ ( 𝜓 → 𝜒 ) ) )