Definition df-cplgr 29772

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 29770	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1568	. . . . 5 class 𝑔
4		cuvtx 29746	. . . . 5 class UnivVtx
5	3, 4	cfv 6536	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 29357	. . . . 5 class Vtx
7	3, 6	cfv 6536	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1569	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2740	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1569	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is used by:  cplgruvtxb  29774