Theorem 3simpa

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

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

Proof

Step	Hyp	Ref	Expression
1		id	$$⊢\left(\phi \wedge \psi \right)\to \left(\phi \wedge \psi \right)$$
2	1	3adant3	$$⊢\left(\phi \wedge \psi \wedge \chi \right)\to \left(\phi \wedge \psi \right)$$