Theorem pm2.31

Description: Theorem *2.31 of WhiteheadRussell p. 104. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm2.31	⊢ ( ( 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) → ( ( 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) )

Proof

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