Definition df-cplgr 29161

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 29159	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1532	. . . . 5 class 𝑔
4		cuvtx 29135	. . . . 5 class UnivVtx
5	3, 4	cfv 6534	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 28749	. . . . 5 class Vtx
7	3, 6	cfv 6534	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1533	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2701	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1533	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  29163