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Metamath Proof Explorer

Theorem snnz

Description: The singleton of a set is not empty. (Contributed by NM, 10-Apr-1994)

		Ref	Expression
	Hypothesis	snnz.1	$⊢ A \in V$
	Assertion	snnz	$⊢ \{A\} \neq \emptyset$

Step	Hyp	Ref	Expression
1		snnz.1	$⊢ A \in V$
2		snnzg	$⊢ A \in V \to \{A\} \neq \emptyset$
3	1 2	ax-mp	$⊢ \{A\} \neq \emptyset$