Definition df-cplgr 27201

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 27199	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1537	. . . . 5 class 𝑔
4		cuvtx 27175	. . . . 5 class UnivVtx
5	3, 4	cfv 6324	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 26789	. . . . 5 class Vtx
7	3, 6	cfv 6324	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1538	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2776	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1538	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  27203