Theorem pm1.5

Description: Axiom *1.5 (Assoc) of WhiteheadRussell p. 96. (Contributed by NM, 3-Jan-2005)

	Ref	Expression
Assertion	pm1.5	⊢ ( ( 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) → ( 𝜓 ∨ ( 𝜑 ∨ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		orc	⊢ ( 𝜑 → ( 𝜑 ∨ 𝜒 ) )
2	1	olcd	⊢ ( 𝜑 → ( 𝜓 ∨ ( 𝜑 ∨ 𝜒 ) ) )
3		olc	⊢ ( 𝜒 → ( 𝜑 ∨ 𝜒 ) )
4	3	orim2i	⊢ ( ( 𝜓 ∨ 𝜒 ) → ( 𝜓 ∨ ( 𝜑 ∨ 𝜒 ) ) )
5	2 4	jaoi	⊢ ( ( 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) → ( 𝜓 ∨ ( 𝜑 ∨ 𝜒 ) ) )