Theorem an21

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

	Ref	Expression
Assertion	an21	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\leftrightarrow \left(\psi \wedge \left(\phi \wedge \chi \right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		biid	$$⊢\left(\phi \wedge \chi \right)\leftrightarrow \left(\phi \wedge \chi \right)$$
2	1	bianassc	$$⊢\left(\psi \wedge \left(\phi \wedge \chi \right)\right)\leftrightarrow \left(\left(\phi \wedge \psi \right)\wedge \chi \right)$$
3	2	bicomi	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\leftrightarrow \left(\psi \wedge \left(\phi \wedge \chi \right)\right)$$