Theorem nbgrssvtx

Description: The neighbors of a vertex K in a graph form a subset of all vertices of the graph. (Contributed by Alexander van der Vekens, 12-Oct-2017) (Revised by AV, 26-Oct-2020) (Revised by AV, 12-Feb-2022)

	Ref	Expression
Hypothesis	nbgrisvtx.v	|- V = ( Vtx ` G )
Assertion	nbgrssvtx	|- ( G NeighbVtx K ) C_ V

Proof

Step	Hyp	Ref	Expression
1		nbgrisvtx.v	|- V = ( Vtx ` G )
2	1	nbgrisvtx	|- ( n e. ( G NeighbVtx K ) -> n e. V )
3	2	ssriv	|- ( G NeighbVtx K ) C_ V