Definition df-edg 15853

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. 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 15852	. 2 class Edg
2		vg	. . 3 setvar 𝑔
3		cvv 2799	. . 3 class V
4	2	cv 1394	. . . . 5 class 𝑔
5		ciedg 15808	. . . . 5 class iEdg
6	4, 5	cfv 5317	. . . 4 class (iEdg‘𝑔)
7	6	crn 4719	. . 3 class ran (iEdg‘𝑔)
8	2, 3, 7	cmpt 4144	. 2 class (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
9	1, 8	wceq 1395	1 wff Edg = (𝑔 ∈ V ↦ ran (iEdg‘𝑔))

This definition is referenced by:  edgvalg  15854  edgopval  15856  edgstruct  15858