Definition df-cplgr 29428

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 29426	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1539	. . . . 5 class 𝑔
4		cuvtx 29402	. . . . 5 class UnivVtx
5	3, 4	cfv 6561	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 29013	. . . . 5 class Vtx
7	3, 6	cfv 6561	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1540	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2714	. 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  29430