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Definition df-edg 28308
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 does not even need 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 28389). 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 28307 . 2 class Edg
2 vg . . 3 setvar 𝑔
3 cvv 3475 . . 3 class V
42cv 1541 . . . . 5 class 𝑔
5 ciedg 28257 . . . . 5 class iEdg
64, 5cfv 6544 . . . 4 class (iEdg‘𝑔)
76crn 5678 . . 3 class ran (iEdg‘𝑔)
82, 3, 7cmpt 5232 . 2 class (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
91, 8wceq 1542 1 wff Edg = (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
Colors of variables: wff setvar class
This definition is referenced by:  edgval  28309
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