Theorem wksv

Description: The class of walks is a set. (Contributed by AV, 15-Jan-2021) (Proof shortened by SN, 11-Dec-2024)

	Ref	Expression
Assertion	wksv	$$⊢\left\{⟨f,p⟩|f\mathrm{Walks}\left(G\right)p\right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		fvex	$$⊢\mathrm{Walks}\left(G\right)\in \mathrm{V}$$
2		opabss	$$⊢\left\{⟨f,p⟩|f\mathrm{Walks}\left(G\right)p\right\}\subseteq \mathrm{Walks}\left(G\right)$$
3	1 2	ssexi	$$⊢\left\{⟨f,p⟩|f\mathrm{Walks}\left(G\right)p\right\}\in \mathrm{V}$$