Theorem simp31

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

	Ref	Expression
Assertion	simp31	$$⊢\left(\phi \wedge \psi \wedge \left(\chi \wedge \theta \wedge \tau \right)\right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		simp1	$$⊢\left(\chi \wedge \theta \wedge \tau \right)\to \chi$$
2	1	3ad2ant3	$$⊢\left(\phi \wedge \psi \wedge \left(\chi \wedge \theta \wedge \tau \right)\right)\to \chi$$