Theorem simp12l

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012)

	Ref	Expression
Assertion	simp12l	$$⊢\left(\left(\chi \wedge \left(\phi \wedge \psi \right)\wedge \theta \right)\wedge \tau \wedge \eta \right)\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		simp2l	$$⊢\left(\chi \wedge \left(\phi \wedge \psi \right)\wedge \theta \right)\to \phi$$
2	1	3ad2ant1	$$⊢\left(\left(\chi \wedge \left(\phi \wedge \psi \right)\wedge \theta \right)\wedge \tau \wedge \eta \right)\to \phi$$