Theorem simp1r1

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

	Ref	Expression
Assertion	simp1r1	$$⊢\left(\left(\theta \wedge \left(\phi \wedge \psi \wedge \chi \right)\right)\wedge \tau \wedge \eta \right)\to \phi$$

Proof

Step	Hyp	Ref	Expression
1		simpr1	$$⊢\left(\theta \wedge \left(\phi \wedge \psi \wedge \chi \right)\right)\to \phi$$
2	1	3ad2ant1	$$⊢\left(\left(\theta \wedge \left(\phi \wedge \psi \wedge \chi \right)\right)\wedge \tau \wedge \eta \right)\to \phi$$