Theorem simpl3r

Description: Simplification of conjunction. (Contributed by NM, 9-Mar-2012) (Proof shortened by Wolf Lammen, 23-Jun-2022)

	Ref	Expression
Assertion	simpl3r	$$⊢\left(\left(\chi \wedge \theta \wedge \left(\phi \wedge \psi \right)\right)\wedge \tau \right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		simplr	$$⊢\left(\left(\phi \wedge \psi \right)\wedge \tau \right)\to \psi$$
2	1	3ad2antl3	$$⊢\left(\left(\chi \wedge \theta \wedge \left(\phi \wedge \psi \right)\right)\wedge \tau \right)\to \psi$$