Definition df-cplgr 27778

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 27776	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1538	. . . . 5 class 𝑔
4		cuvtx 27752	. . . . 5 class UnivVtx
5	3, 4	cfv 6433	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 27366	. . . . 5 class Vtx
7	3, 6	cfv 6433	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1539	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2715	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1539	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  27780