Theorem 3simpc

Description: Simplification of triple conjunction. (Contributed by NM, 21-Apr-1994) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 21-Jun-2022)

	Ref	Expression
Assertion	3simpc	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\psi \wedge \chi \right)$$

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\psi \wedge \chi \right)\to \left(\psi \wedge \chi \right)$$
2	1	3adant1	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\psi \wedge \chi \right)$$