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Metamath Proof Explorer

Theorem n0i

Description: If a class has elements, then it is not empty. (Contributed by NM, 31-Dec-1993)

		Ref	Expression
	Assertion	n0i	$⊢ B \in A \to \neg A = \emptyset$

Step	Hyp	Ref	Expression
1		nel02	$⊢ A = \emptyset \to \neg B \in A$
2	1	con2i	$⊢ B \in A \to \neg A = \emptyset$