Definition df-cplgr 29727

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 29725	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1567	. . . . 5 class 𝑔
4		cuvtx 29701	. . . . 5 class UnivVtx
5	3, 4	cfv 6536	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 29312	. . . . 5 class Vtx
7	3, 6	cfv 6536	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1568	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2739	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1568	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  29729