Theorem simprlr

Description: Simplification of a conjunction. (Contributed by Jeff Hankins, 28-Jul-2009)

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

Proof

Step	Hyp	Ref	Expression
1		simpr	$$⊢\left(\psi \wedge \chi \right)\to \chi$$
2	1	ad2antrl	$$⊢\left(\phi \wedge \left(\left(\psi \wedge \chi \right)\wedge \theta \right)\right)\to \chi$$