Definition df-cplgr 26716

Description: Define the class of all complete "graphs". A class/graph is called complete if every pair of distinct vertices is connected by an edge, i.e., each vertex has all other vertices as neighbors or, in other words, each vertex is a universal vertex. (Contributed by AV, 24-Oct-2020.) (Revised by TA, 15-Feb-2022.)

Assertion

Ref	Expression
df-cplgr	⊢ ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

Detailed syntax breakdown of Definition df-cplgr

Step	Hyp	Ref	Expression
1		ccplgr 26714	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1655	. . . . 5 class 𝑔
4		cuvtx 26690	. . . . 5 class UnivVtx
5	3, 4	cfv 6127	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 26301	. . . . 5 class Vtx
7	3, 6	cfv 6127	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1656	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2811	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1656	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  26718