Theorem vtxvalprc

Description: Degenerated case 4 for vertices: The set of vertices of a proper class is the empty set. (Contributed by AV, 12-Oct-2020)

	Ref	Expression
Assertion	vtxvalprc	$$⊢C\notin \mathrm{V}\to \mathrm{Vtx}\left(C\right)=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		df-nel	$$⊢C\notin \mathrm{V}\leftrightarrow \neg C\in \mathrm{V}$$
2		fvprc	$$⊢\neg C\in \mathrm{V}\to \mathrm{Vtx}\left(C\right)=\varnothing$$
3	1 2	sylbi	$$⊢C\notin \mathrm{V}\to \mathrm{Vtx}\left(C\right)=\varnothing$$