Theorem 1vgrex

Description: A graph with at least one vertex is a set. (Contributed by AV, 2-Mar-2021)

	Ref	Expression
Hypothesis	1vgrex.v	$$⊢V=\mathrm{Vtx}\left(G\right)$$
Assertion	1vgrex	$$⊢N\in V\to G\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		1vgrex.v	$$⊢V=\mathrm{Vtx}\left(G\right)$$
2		elfvex	$$⊢N\in \mathrm{Vtx}\left(G\right)\to G\in \mathrm{V}$$
3	2 1	eleq2s	$$⊢N\in V\to G\in \mathrm{V}$$