Theorem simp12

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

	Ref	Expression
Assertion	simp12	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \wedge \tau \right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		simp2	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \psi$$
2	1	3ad2ant1	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \wedge \tau \right)\to \psi$$