Theorem 3orcomb

Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011) (Proof shortened by Wolf Lammen, 8-Apr-2022)

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

Proof

Step	Hyp	Ref	Expression
1		3orcoma	⊢ ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) ↔ ( 𝜓 ∨ 𝜑 ∨ 𝜒 ) )
2		3orrot	⊢ ( ( 𝜓 ∨ 𝜑 ∨ 𝜒 ) ↔ ( 𝜑 ∨ 𝜒 ∨ 𝜓 ) )
3	1 2	bitri	⊢ ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) ↔ ( 𝜑 ∨ 𝜒 ∨ 𝜓 ) )