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Metamath Proof Explorer

Theorem snn0d

Description: The singleton of a set is not empty. (Contributed by Glauco Siliprandi, 3-Mar-2021)

		Ref	Expression
	Hypothesis	snn0d.1	$⊢ φ \to A \in V$
	Assertion	snn0d	$⊢ φ \to \{A\} \neq \emptyset$

Step	Hyp	Ref	Expression
1		snn0d.1	$⊢ φ \to A \in V$
2		snnzg	$⊢ A \in V \to \{A\} \neq \emptyset$
3	1 2	syl	$⊢ φ \to \{A\} \neq \emptyset$