Theorem simp3ll

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

	Ref	Expression
Assertion	simp3ll	$$⊢\left(\theta \wedge \tau \wedge \left(\left(\phi \wedge \psi \right)\wedge \chi \right)\right)\to \phi$$

Proof

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