Theorem 3ancomb

Description: Commutation law for triple conjunction. (Contributed by NM, 21-Apr-1994) (Revised to shorten 3anrot by Wolf Lammen, 9-Jun-2022.)

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

Proof

Step	Hyp	Ref	Expression
1		df-3an	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) )
2		3anan32	⊢ ( ( 𝜑 ∧ 𝜒 ∧ 𝜓 ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) )
3	1 2	bitr4i	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( 𝜑 ∧ 𝜒 ∧ 𝜓 ) )