Definition df-cplgr 29505

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 29503	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1546	. . . . 5 class 𝑔
4		cuvtx 29479	. . . . 5 class UnivVtx
5	3, 4	cfv 6492	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 29090	. . . . 5 class Vtx
7	3, 6	cfv 6492	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1547	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2718	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1547	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is referenced by:  cplgruvtxb  29507