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Definition df-edg 27006
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 27087). 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 27005 . 2 class Edg
2 vg . . 3 setvar 𝑔
3 cvv 3400 . . 3 class V
42cv 1541 . . . . 5 class 𝑔
5 ciedg 26955 . . . . 5 class iEdg
64, 5cfv 6350 . . . 4 class (iEdg‘𝑔)
76crn 5536 . . 3 class ran (iEdg‘𝑔)
82, 3, 7cmpt 5120 . 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  27007
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