Theorem simpl2

Description: Simplification of conjunction. (Contributed by Jeff Hankins, 17-Nov-2009) (Proof shortened by Wolf Lammen, 23-Jun-2022)

	Ref	Expression
Assertion	simpl2	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		simpl	$$⊢\left(\psi \wedge \theta \right)\to \psi$$
2	1	3ad2antl2	$$⊢\left(\left(\phi \wedge \psi \wedge \chi \right)\wedge \theta \right)\to \psi$$