Theorem 3anrot

Description: Rotation law for triple conjunction. (Contributed by NM, 8-Apr-1994) (Proof shortened by Wolf Lammen, 9-Jun-2022)

	Ref	Expression
Assertion	3anrot	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜑 ) )

Proof

Step	Hyp	Ref	Expression
1		3ancoma	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) )
2		3ancomb	⊢ ( ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜑 ) )
3	1 2	bitri	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜒 ∧ 𝜑 ) )