Theorem pm2.81

Description: Theorem *2.81 of WhiteheadRussell p. 108. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm2.81	⊢ ( ( 𝜓 → ( 𝜒 → 𝜃 ) ) → ( ( 𝜑 ∨ 𝜓 ) → ( ( 𝜑 ∨ 𝜒 ) → ( 𝜑 ∨ 𝜃 ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		orim2	⊢ ( ( 𝜓 → ( 𝜒 → 𝜃 ) ) → ( ( 𝜑 ∨ 𝜓 ) → ( 𝜑 ∨ ( 𝜒 → 𝜃 ) ) ) )
2		pm2.76	⊢ ( ( 𝜑 ∨ ( 𝜒 → 𝜃 ) ) → ( ( 𝜑 ∨ 𝜒 ) → ( 𝜑 ∨ 𝜃 ) ) )
3	1 2	syl6	⊢ ( ( 𝜓 → ( 𝜒 → 𝜃 ) ) → ( ( 𝜑 ∨ 𝜓 ) → ( ( 𝜑 ∨ 𝜒 ) → ( 𝜑 ∨ 𝜃 ) ) ) )