Definition df-cplgr 29390

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 29388	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1539	. . . . 5 class 𝑔
4		cuvtx 29364	. . . . 5 class UnivVtx
5	3, 4	cfv 6531	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 28975	. . . . 5 class Vtx
7	3, 6	cfv 6531	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1540	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2713	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1540	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  29392