Theorem simpr2l

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

	Ref	Expression
Assertion	simpr2l	$$⊢\left(\tau \wedge \left(\chi \wedge \left(\phi \wedge \psi \right)\wedge \theta \right)\right)\to \phi$$

Proof

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