Theorem 3orrot

Description: Rotation law for triple disjunction. (Contributed by NM, 4-Apr-1995)

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

Proof

Step	Hyp	Ref	Expression
1		orcom	⊢ ( ( 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) ↔ ( ( 𝜓 ∨ 𝜒 ) ∨ 𝜑 ) )
2		3orass	⊢ ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) ↔ ( 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) )
3		df-3or	⊢ ( ( 𝜓 ∨ 𝜒 ∨ 𝜑 ) ↔ ( ( 𝜓 ∨ 𝜒 ) ∨ 𝜑 ) )
4	1 2 3	3bitr4i	⊢ ( ( 𝜑 ∨ 𝜓 ∨ 𝜒 ) ↔ ( 𝜓 ∨ 𝜒 ∨ 𝜑 ) )