Theorem snn0d

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

	Ref	Expression
Hypothesis	snn0d.1	$$⊢\phi \to A\in V$$
Assertion	snn0d	$$⊢\phi \to \left\{A\right\}\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		snn0d.1	$$⊢\phi \to A\in V$$
2		snnzg	$$⊢A\in V\to \left\{A\right\}\ne \varnothing$$
3	1 2	syl	$$⊢\phi \to \left\{A\right\}\ne \varnothing$$