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Definition df-edg 25865
 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 for any ordered pairs as the range of its second component (which even needs not to be a function). Therefore, this definition could also be used for hypergraphs and multigraphs. In these cases, however, the (possibly more than one) edges connecting the same vertices could not be distinguished anymore. Therefore, this definition should only be used for undirected simple graphs. (Contributed by AV, 1-Jan-2020.)
Assertion
Ref Expression
df-edg Edges = (𝑔 ∈ V ↦ ran (2nd𝑔))

Detailed syntax breakdown of Definition df-edg
StepHypRef Expression
1 cedg 25860 . 2 class Edges
2 vg . . 3 setvar 𝑔
3 cvv 3173 . . 3 class V
42cv 1474 . . . . 5 class 𝑔
5 c2nd 7058 . . . . 5 class 2nd
64, 5cfv 5804 . . . 4 class (2nd𝑔)
76crn 5039 . . 3 class ran (2nd𝑔)
82, 3, 7cmpt 4643 . 2 class (𝑔 ∈ V ↦ ran (2nd𝑔))
91, 8wceq 1475 1 wff Edges = (𝑔 ∈ V ↦ ran (2nd𝑔))
 Colors of variables: wff setvar class This definition is referenced by:  edgval  25868
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