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Definition df-cplgr 26716
 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
StepHypRef Expression
1 ccplgr 26714 . 2 class ComplGraph
2 vg . . . . . 6 setvar 𝑔
32cv 1655 . . . . 5 class 𝑔
4 cuvtx 26690 . . . . 5 class UnivVtx
53, 4cfv 6127 . . . 4 class (UnivVtx‘𝑔)
6 cvtx 26301 . . . . 5 class Vtx
73, 6cfv 6127 . . . 4 class (Vtx‘𝑔)
85, 7wceq 1656 . . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
98, 2cab 2811 . 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
101, 9wceq 1656 1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
 Colors of variables: wff setvar class This definition is referenced by:  cplgruvtxb  26718
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