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Metamath Proof Explorer

Theorem fusgrvtxfi

Description: A finite simple graph has a finite set of vertices. (Contributed by AV, 16-Dec-2020)

		Ref	Expression
	Hypothesis	isfusgr.v	$⊢ V = Vtx (G)$
	Assertion	fusgrvtxfi	$⊢ G \in FinUSGraph \to V \in Fin$

Step	Hyp	Ref	Expression
1		isfusgr.v	$⊢ V = Vtx (G)$
2	1	isfusgr	$⊢ G \in FinUSGraph \leftrightarrow (G \in USGraph \land V \in Fin)$
3	2	simprbi	$⊢ G \in FinUSGraph \to V \in Fin$