Definition df-edg 29142

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 29223). 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

Step	Hyp	Ref	Expression
1		cedg 29141	. 2 class Edg
2		vg	. . 3 setvar 𝑔
3		cvv 3432	. . 3 class V
4	2	cv 1546	. . . . 5 class 𝑔
5		ciedg 29091	. . . . 5 class iEdg
6	4, 5	cfv 6492	. . . 4 class (iEdg‘𝑔)
7	6	crn 5626	. . 3 class ran (iEdg‘𝑔)
8	2, 3, 7	cmpt 5160	. 2 class (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
9	1, 8	wceq 1547	1 wff Edg = (𝑔 ∈ V ↦ ran (iEdg‘𝑔))

This definition is referenced by:  edgval  29143