Theorem 3ancoma

Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994) (Proof shortened by Wolf Lammen, 5-Jun-2022)

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

Proof

Step	Hyp	Ref	Expression
1		3anan12	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜓 ∧ ( 𝜑 ∧ 𝜒 ) ) )
2		3anass	⊢ ( ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) ↔ ( 𝜓 ∧ ( 𝜑 ∧ 𝜒 ) ) )
3	1 2	bitr4i	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜓 ∧ 𝜑 ∧ 𝜒 ) )