Theorem n0ii

Description: If a class has elements, then it is not empty. Inference associated with n0i . (Contributed by BJ, 15-Jul-2021)

	Ref	Expression
Hypothesis	n0ii.1	$$⊢A\in B$$
Assertion	n0ii	$$⊢\neg B=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		n0ii.1	$$⊢A\in B$$
2		n0i	$$⊢A\in B\to \neg B=\varnothing$$
3	1 2	ax-mp	$$⊢\neg B=\varnothing$$