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Definition df-edg 26176
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 26260). 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 26175 . 2 class Edg
2 vg . . 3 setvar 𝑔
3 cvv 3402 . . 3 class V
42cv 1636 . . . . 5 class 𝑔
5 ciedg 26111 . . . . 5 class iEdg
64, 5cfv 6110 . . . 4 class (iEdg‘𝑔)
76crn 5325 . . 3 class ran (iEdg‘𝑔)
82, 3, 7cmpt 4934 . 2 class (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
91, 8wceq 1637 1 wff Edg = (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
Colors of variables: wff setvar class
This definition is referenced by:  edgval  26177  edgvalOLD  26178
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