Theorem nel1nelin

Description: Membership in an intersection implies membership in the first set. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Assertion	nel1nelin	$$⊢\neg A\in B\to \neg A\in \left(B\cap C\right)$$

Proof

Step	Hyp	Ref	Expression
1		elinel1	$$⊢A\in \left(B\cap C\right)\to A\in B$$
2	1	con3i	$$⊢\neg A\in B\to \neg A\in \left(B\cap C\right)$$