Definition df-cplgr 30022

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 30020	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1569	. . . . 5 class 𝑔
4		cuvtx 29996	. . . . 5 class UnivVtx
5	3, 4	cfv 6558	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 29604	. . . . 5 class Vtx
7	3, 6	cfv 6558	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1570	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2741	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1570	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is used by:  cplgruvtxb  30024