Metamath Proof Explorer


Theorem uvtxnbgrss

Description: A universal vertex has all other vertices as neighbors. (Contributed by Alexander van der Vekens, 14-Oct-2017) (Revised by AV, 30-Oct-2020)

Ref Expression
Hypothesis uvtxel.v V = Vtx G
Assertion uvtxnbgrss N UnivVtx G V N G NeighbVtx N

Proof

Step Hyp Ref Expression
1 uvtxel.v V = Vtx G
2 1 vtxnbuvtx N UnivVtx G n V N n G NeighbVtx N
3 dfss3 V N G NeighbVtx N n V N n G NeighbVtx N
4 2 3 sylibr N UnivVtx G V N G NeighbVtx N