Definition df-cplgr 29480

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 29478	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1541	. . . . 5 class 𝑔
4		cuvtx 29454	. . . . 5 class UnivVtx
5	3, 4	cfv 6499	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 29065	. . . . 5 class Vtx
7	3, 6	cfv 6499	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1542	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2715	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1542	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  29482