Definition df-cplgr 29338

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 29336	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1539	. . . . 5 class 𝑔
4		cuvtx 29312	. . . . 5 class UnivVtx
5	3, 4	cfv 6511	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 28923	. . . . 5 class Vtx
7	3, 6	cfv 6511	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1540	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2707	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1540	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  29340