Theorem 0wlk0

Description: There is no walk for the empty set, i.e. in a null graph. (Contributed by Alexander van der Vekens, 2-Sep-2018) (Revised by AV, 5-Mar-2021)

	Ref	Expression
Assertion	0wlk0	$$⊢\mathrm{Walks}\left(\varnothing \right)=\varnothing$$

Proof

Step	Hyp	Ref	Expression
1		vtxval0	$$⊢\mathrm{Vtx}\left(\varnothing \right)=\varnothing$$
2		g0wlk0	$$⊢\mathrm{Vtx}\left(\varnothing \right)=\varnothing \to \mathrm{Walks}\left(\varnothing \right)=\varnothing$$
3	1 2	ax-mp	$$⊢\mathrm{Walks}\left(\varnothing \right)=\varnothing$$