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Definition df-cplgr 26516
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 26514 . 2 class ComplGraph
2 vg . . . . . 6 setvar 𝑔
32cv 1631 . . . . 5 class 𝑔
4 cuvtx 26485 . . . . 5 class UnivVtx
53, 4cfv 6049 . . . 4 class (UnivVtx‘𝑔)
6 cvtx 26073 . . . . 5 class Vtx
73, 6cfv 6049 . . . 4 class (Vtx‘𝑔)
85, 7wceq 1632 . . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
98, 2cab 2746 . 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
101, 9wceq 1632 1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
Colors of variables: wff setvar class
This definition is referenced by:  cplgruvtxb  26518
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