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Metamath Proof Explorer

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	$⊢ \neg B = \emptyset$

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