Theorem 13an22anass

Description: Associative law for four conjunctions with a triple conjunction. (Contributed by Thierry Arnoux, 21-Jan-2025) (Proof shortened by Wolf Lammen, 31-Oct-2026)

	Ref	Expression
Assertion	13an22anass	⊢ ( ( 𝜑 ∧ ( 𝜓 ∧ 𝜒 ∧ 𝜃 ) ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ ( 𝜒 ∧ 𝜃 ) ) )

Proof

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