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Metamath Proof Explorer

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 ) )

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 ) )