Theorem simpr23

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012) (Proof shortened by Wolf Lammen, 24-Jun-2022)

	Ref	Expression
Assertion	simpr23	$$⊢\left(\eta \wedge \left(\theta \wedge \left(\phi \wedge \psi \wedge \chi \right)\wedge \tau \right)\right)\to \chi$$

Proof

Step	Hyp	Ref	Expression
1		simpr3	$$⊢\left(\eta \wedge \left(\phi \wedge \psi \wedge \chi \right)\right)\to \chi$$
2	1	3ad2antr2	$$⊢\left(\eta \wedge \left(\theta \wedge \left(\phi \wedge \psi \wedge \chi \right)\wedge \tau \right)\right)\to \chi$$