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Definition df-edga 40350
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 40360). 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-edga Edg = (𝑔 ∈ V ↦ ran (iEdg‘𝑔))

Detailed syntax breakdown of Definition df-edga
StepHypRef Expression
1 cedga 40349 . 2 class Edg
2 vg . . 3 setvar 𝑔
3 cvv 3168 . . 3 class V
42cv 1473 . . . . 5 class 𝑔
5 ciedg 40228 . . . . 5 class iEdg
64, 5cfv 5786 . . . 4 class (iEdg‘𝑔)
76crn 5025 . . 3 class ran (iEdg‘𝑔)
82, 3, 7cmpt 4633 . 2 class (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
91, 8wceq 1474 1 wff Edg = (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
Colors of variables: wff setvar class
This definition is referenced by:  edgaval  40351
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