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	⊢ ( Walks ‘ ∅ ) = ∅

Proof

Step	Hyp	Ref	Expression
1		vtxval0	⊢ ( Vtx ‘ ∅ ) = ∅
2		g0wlk0	⊢ ( ( Vtx ‘ ∅ ) = ∅ → ( Walks ‘ ∅ ) = ∅ )
3	1 2	ax-mp	⊢ ( Walks ‘ ∅ ) = ∅