Theorem elnel

Description: A class cannot be an element of one of its elements. (Contributed by AV, 14-Jun-2022)

	Ref	Expression
Assertion	elnel	$$⊢A\in B\to B\notin A$$

Proof

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