Definition df-cplgr 29993

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 29991	. 2 class ComplGraph
2		vg	. . . . . 6 setvar 𝑔
3	2	cv 1568	. . . . 5 class 𝑔
4		cuvtx 29967	. . . . 5 class UnivVtx
5	3, 4	cfv 6538	. . . 4 class (UnivVtx‘𝑔)
6		cvtx 29575	. . . . 5 class Vtx
7	3, 6	cfv 6538	. . . 4 class (Vtx‘𝑔)
8	5, 7	wceq 1569	. . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
9	8, 2	cab 2738	. 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
10	1, 9	wceq 1569	1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}

This definition is used by:  cplgruvtxb  29995