Theorem an32

Description: A rearrangement of conjuncts. (Contributed by NM, 12-Mar-1995) (Proof shortened by Wolf Lammen, 25-Dec-2012)

	Ref	Expression
Assertion	an32	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\leftrightarrow \left(\left(\phi \wedge \chi \right)\wedge \psi \right)$$

Proof

Step	Hyp	Ref	Expression
1		an21	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\leftrightarrow \left(\psi \wedge \left(\phi \wedge \chi \right)\right)$$
2	1	biancomi	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \chi \right)\leftrightarrow \left(\left(\phi \wedge \chi \right)\wedge \psi \right)$$