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 e// B -> A e/ B )

Proof

Step	Hyp	Ref	Expression
1		nelbrim	|- ( A e// B -> -. A e. B )
2		df-nel	|- ( A e/ B <-> -. A e. B )
3	1 2	sylibr	|- ( A e// B -> A e/ B )