Theorem simp22

Description: Simplification of doubly triple conjunction. (Contributed by NM, 17-Nov-2011)

	Ref	Expression
Assertion	simp22	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\wedge \tau \right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		simp2	$$⊢\left(\psi \wedge \chi \wedge \theta \right)\to \chi$$
2	1	3ad2ant2	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\wedge \tau \right)\to \chi$$