Theorem nelbrnelim

Description: If a set is related to another set by the negated membership relation, then it is not a member of the other set. (Contributed by AV, 26-Dec-2021)

	Ref	Expression
Assertion	nelbrnelim	$$⊢A\notin B\to A\notin B$$

Proof

Step	Hyp	Ref	Expression
1		nelbrim	$$⊢A\notin B\to \neg A\in B$$
2		df-nel	$$⊢A\notin B\leftrightarrow \neg A\in B$$
3	1 2	sylibr	$$⊢A\notin B\to A\notin B$$