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Metamath Proof Explorer

Theorem clwlkiswlk

Description: A closed walk is a walk (in an undirected graph). (Contributed by Alexander van der Vekens, 15-Mar-2018) (Revised by AV, 16-Feb-2021) (Proof shortened by AV, 30-Oct-2021)

		Ref	Expression
	Assertion	clwlkiswlk	$⊢ F ClWalks (G) P \to F Walks (G) P$

Proof

Step	Hyp	Ref	Expression
1		isclwlk	$⊢ F ClWalks (G) P \leftrightarrow (F Walks (G) P \land P (0) = P (\|F\|))$
2	1	simplbi	$⊢ F ClWalks (G) P \to F Walks (G) P$