Theorem clnbgrn0

Description: The closed neighborhood of a vertex is never empty. (Contributed by AV, 16-May-2025)

	Ref	Expression
Hypothesis	clnbgrn0.v	$$⊢V=\mathrm{Vtx}\left(G\right)$$
Assertion	clnbgrn0	Could not format assertion : No typesetting found for |- ( N e. V -> ( G ClNeighbVtx N ) =/= (/) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		clnbgrn0.v	$$⊢V=\mathrm{Vtx}\left(G\right)$$
2	1	clnbgrvtxel	Could not format ( N e. V -> N e. ( G ClNeighbVtx N ) ) : No typesetting found for |- ( N e. V -> N e. ( G ClNeighbVtx N ) ) with typecode |-
3		ne0i	Could not format ( N e. ( G ClNeighbVtx N ) -> ( G ClNeighbVtx N ) =/= (/) ) : No typesetting found for |- ( N e. ( G ClNeighbVtx N ) -> ( G ClNeighbVtx N ) =/= (/) ) with typecode |-
4	2 3	syl	Could not format ( N e. V -> ( G ClNeighbVtx N ) =/= (/) ) : No typesetting found for |- ( N e. V -> ( G ClNeighbVtx N ) =/= (/) ) with typecode |-