Theorem 3orcoma

Description: Commutation law for triple disjunction. (Contributed by Mario Carneiro, 4-Sep-2016)

	Ref	Expression
Assertion	3orcoma	⊢ ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) ↔ ( 𝜓 ∨ 𝜑 ∨ 𝜒 ) )

Proof

Step	Hyp	Ref	Expression
1		or12	⊢ ( ( 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) ↔ ( 𝜓 ∨ ( 𝜑 ∨ 𝜒 ) ) )
2		3orass	⊢ ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) ↔ ( 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) )
3		3orass	⊢ ( ( 𝜓 ∨ 𝜑 ∨ 𝜒 ) ↔ ( 𝜓 ∨ ( 𝜑 ∨ 𝜒 ) ) )
4	1 2 3	3bitr4i	⊢ ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) ↔ ( 𝜓 ∨ 𝜑 ∨ 𝜒 ) )