Theorem 3anan32

Description: Convert triple conjunction to conjunction, then commute. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (Shortened by Garrett Katz, 15-Jun-2026.)

	Ref	Expression
Assertion	3anan32	⊢ ( ( 𝜑 ∧ 𝜓 ∧ 𝜒 ) ↔ ( ( 𝜑 ∧ 𝜒 ) ∧ 𝜓 ) )

Proof

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