Definition df-cplgr 29400

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 29398	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1540	. . . . 5 class 𝑔
4		cuvtx 29374	. . . . 5 class UnivVtx
5	3, 4	cfv 6489	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 28985	. . . . 5 class Vtx
7	3, 6	cfv 6489	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1541	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2711	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1541	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  29402