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Definition df-edg 25921
Description: Define the class of edges of a graph, see also definition "E = E(G)" in section I.1 of [Bollobas] p. 1. This definition is very general: It defines edges of a class as the range of its edge function (which even needs not to be a function). Therefore, this definition could also be used for hypergraphs, pseudographs and multigraphs. In these cases, however, the (possibly more than one) edges connecting the same vertices could not be distinguished anymore. In some cases, this is no problem, so theorems with Edg are meaningful nevertheless (e.g., edguhgr 26005). Usually, however, this definition is used only for undirected simple (hyper-/pseudo-)graphs (with or without loops). (Contributed by AV, 1-Jan-2020.) (Revised by AV, 13-Oct-2020.)
Assertion
Ref Expression
df-edg Edg = (𝑔 ∈ V ↦ ran (iEdg‘𝑔))

Detailed syntax breakdown of Definition df-edg
StepHypRef Expression
1 cedg 25920 . 2 class Edg
2 vg . . 3 setvar 𝑔
3 cvv 3195 . . 3 class V
42cv 1480 . . . . 5 class 𝑔
5 ciedg 25856 . . . . 5 class iEdg
64, 5cfv 5876 . . . 4 class (iEdg‘𝑔)
76crn 5105 . . 3 class ran (iEdg‘𝑔)
82, 3, 7cmpt 4720 . 2 class (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
91, 8wceq 1481 1 wff Edg = (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
Colors of variables: wff setvar class
This definition is referenced by:  edgval  25922  edgvalOLD  25923
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