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Metamath Proof Explorer

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	$⊢ Walks (\emptyset) = \emptyset$

Proof

Step	Hyp	Ref	Expression
1		vtxval0	$⊢ Vtx (\emptyset) = \emptyset$
2		g0wlk0	$⊢ Vtx (\emptyset) = \emptyset \to Walks (\emptyset) = \emptyset$
3	1 2	ax-mp	$⊢ Walks (\emptyset) = \emptyset$