Theorem opvtxfvi

Description: The set of vertices of a graph represented as an ordered pair of vertices and indexed edges as function value. (Contributed by AV, 4-Mar-2021)

	Ref	Expression
Hypotheses	opvtxfvi.v	$$⊢V\in \mathrm{V}$$
	opvtxfvi.e	$$⊢E\in \mathrm{V}$$
Assertion	opvtxfvi	$$⊢\mathrm{Vtx}\left(⟨V,E⟩\right)=V$$

Proof

Step	Hyp	Ref	Expression
1		opvtxfvi.v	$$⊢V\in \mathrm{V}$$
2		opvtxfvi.e	$$⊢E\in \mathrm{V}$$
3		opvtxfv	$$⊢\left(V\in \mathrm{V}\wedge E\in \mathrm{V}\right)\to \mathrm{Vtx}\left(⟨V,E⟩\right)=V$$
4	1 2 3	mp2an	$$⊢\mathrm{Vtx}\left(⟨V,E⟩\right)=V$$