Theorem pm2.74

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

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

Proof

Step	Hyp	Ref	Expression
1		orel2	⊢ ( ¬ 𝜓 → ( ( 𝜑 ∨ 𝜓 ) → 𝜑 ) )
2		ax-1	⊢ ( 𝜑 → ( ( 𝜑 ∨ 𝜓 ) → 𝜑 ) )
3	1 2	ja	⊢ ( ( 𝜓 → 𝜑 ) → ( ( 𝜑 ∨ 𝜓 ) → 𝜑 ) )
4	3	orim1d	⊢ ( ( 𝜓 → 𝜑 ) → ( ( ( 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) → ( 𝜑 ∨ 𝜒 ) ) )