Definition df-cplgr 29223

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 29221	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1533	. . . . 5 class 𝑔
4		cuvtx 29197	. . . . 5 class UnivVtx
5	3, 4	cfv 6548	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 28808	. . . . 5 class Vtx
7	3, 6	cfv 6548	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1534	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2705	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1534	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  29225