Definition df-edg 28973

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 29054). 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 28972	. 2 class Edg
2		vg	. . 3 setvar 𝑔
3		cvv 3459	. . 3 class V
4	2	cv 1539	. . . . 5 class 𝑔
5		ciedg 28922	. . . . 5 class iEdg
6	4, 5	cfv 6530	. . . 4 class (iEdg‘𝑔)
7	6	crn 5655	. . 3 class ran (iEdg‘𝑔)
8	2, 3, 7	cmpt 5201	. 2 class (𝑔 ∈ V ↦ ran (iEdg‘𝑔))
9	1, 8	wceq 1540	1 wff Edg = (𝑔 ∈ V ↦ ran (iEdg‘𝑔))

This definition is referenced by:  edgval  28974