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Definition df-cplgr 27120
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 27118 . 2 class ComplGraph
2 vg . . . . . 6 setvar 𝑔
32cv 1527 . . . . 5 class 𝑔
4 cuvtx 27094 . . . . 5 class UnivVtx
53, 4cfv 6348 . . . 4 class (UnivVtx‘𝑔)
6 cvtx 26708 . . . . 5 class Vtx
73, 6cfv 6348 . . . 4 class (Vtx‘𝑔)
85, 7wceq 1528 . . 3 wff (UnivVtx‘𝑔) = (Vtx‘𝑔)
98, 2cab 2796 . 2 class {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
101, 9wceq 1528 1 wff ComplGraph = {𝑔 ∣ (UnivVtx‘𝑔) = (Vtx‘𝑔)}
Colors of variables: wff setvar class
This definition is referenced by:  cplgruvtxb  27122
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