Theorem an3

Description: A rearrangement of conjuncts. (Contributed by Rodolfo Medina, 25-Sep-2010)

	Ref	Expression
Assertion	an3	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \left(\chi \wedge \theta \right)\right)\to \left(\phi \wedge \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		an43	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \left(\chi \wedge \theta \right)\right)\leftrightarrow \left(\left(\phi \wedge \theta \right)\wedge \left(\psi \wedge \chi \right)\right)$$
2	1	simplbi	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \left(\chi \wedge \theta \right)\right)\to \left(\phi \wedge \theta \right)$$