Theorem elneq

Description: A class is not equal to any of its elements. (Contributed by AV, 14-Jun-2022)

	Ref	Expression
Assertion	elneq	$$⊢A\in B\to A\ne B$$

Proof

Step	Hyp	Ref	Expression
1		elirr	$$⊢\neg B\in B$$
2		nelelne	$$⊢\neg B\in B\to \left(A\in B\to A\ne B\right)$$
3	1 2	ax-mp	$$⊢A\in B\to A\ne B$$