Theorem snnz

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

	Ref	Expression
Hypothesis	snnz.1	$$⊢A\in \mathrm{V}$$
Assertion	snnz	$$⊢\left\{A\right\}\ne \varnothing$$

Proof

Step	Hyp	Ref	Expression
1		snnz.1	$$⊢A\in \mathrm{V}$$
2		snnzg	$$⊢A\in \mathrm{V}\to \left\{A\right\}\ne \varnothing$$
3	1 2	ax-mp	$$⊢\left\{A\right\}\ne \varnothing$$