Theorem an21

Description: Swap two conjuncts. (Contributed by Peter Mazsa, 18-Sep-2022)

	Ref	Expression
Assertion	an21	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ ( 𝜓 ∧ ( 𝜑 ∧ 𝜒 ) ) )

Proof

Step	Hyp	Ref	Expression
1		biid	⊢ ( ( 𝜑 ∧ 𝜒 ) ↔ ( 𝜑 ∧ 𝜒 ) )
2	1	bianassc	⊢ ( ( 𝜓 ∧ ( 𝜑 ∧ 𝜒 ) ) ↔ ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) )
3	2	bicomi	⊢ ( ( ( 𝜑 ∧ 𝜓 ) ∧ 𝜒 ) ↔ ( 𝜓 ∧ ( 𝜑 ∧ 𝜒 ) ) )