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Metamath Proof Explorer

Theorem clnbgrssvtx

Description: The closed neighborhood of a vertex K in a graph is a subset of all vertices of the graph. (Contributed by AV, 9-May-2025)

		Ref	Expression
	Hypothesis	clnbgrvtxel.v	$⊢ V = Vtx (G)$
	Assertion	clnbgrssvtx	$⊢ G ClNeighbVtx K \subseteq V$

Step	Hyp	Ref	Expression
1		clnbgrvtxel.v	$⊢ V = Vtx (G)$
2	1	clnbgrisvtx	$⊢ n \in (G ClNeighbVtx K) \to n \in V$
3	2	ssriv	$⊢ G ClNeighbVtx K \subseteq V$