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Definition df-edg 26766
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 26847). 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 26765 . 2 class Edg
2 vg . . 3 setvar 𝑔
3 cvv 3500 . . 3 class V
42cv 1529 . . . . 5 class 𝑔
5 ciedg 26715 . . . . 5 class iEdg
64, 5cfv 6354 . . . 4 class (iEdg‘𝑔)
76crn 5555 . . 3 class ran (iEdg‘𝑔)
82, 3, 7cmpt 5143 . 2 class (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
91, 8wceq 1530 1 wff Edg = (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
Colors of variables: wff setvar class
This definition is referenced by:  edgval  26767
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