wlkoniswlk

Description: A walk between two vertices is a walk. (Contributed by Alexander van der Vekens, 12-Dec-2017) (Revised by AV, 2-Jan-2021)

		Ref	Expression
	Assertion	wlkoniswlk	$⊢ F (A WalksOn (G) B) P \to F Walks (G) P$

Step	Hyp	Ref	Expression
1		eqid	$⊢ Vtx (G) = Vtx (G)$
2	1	wlkonprop	$⊢ F (A WalksOn (G) B) P \to ((G \in V \land A \in Vtx (G) \land B \in Vtx (G)) \land (F \in V \land P \in V) \land (F Walks (G) P \land P (0) = A \land P (\|F\|) = B))$
3		simp31	$⊢ ((G \in V \land A \in Vtx (G) \land B \in Vtx (G)) \land (F \in V \land P \in V) \land (F Walks (G) P \land P (0) = A \land P (\|F\|) = B)) \to F Walks (G) P$
4	2 3	syl	$⊢ F (A WalksOn (G) B) P \to F Walks (G) P$

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