Definition df-cplgr 29446

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 29444	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1536	. . . . 5 class 𝑔
4		cuvtx 29420	. . . . 5 class UnivVtx
5	3, 4	cfv 6573	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 29031	. . . . 5 class Vtx
7	3, 6	cfv 6573	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1537	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2717	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1537	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  29448