Theorem simpr1

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

	Ref	Expression
Assertion	simpr1	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\right)\to \psi$$

Proof

Step	Hyp	Ref	Expression
1		simpr	$$⊢\left(\phi \wedge \psi \right)\to \psi$$
2	1	3ad2antr1	$$⊢\left(\phi \wedge \left(\psi \wedge \chi \wedge \theta \right)\right)\to \psi$$