Definition df-edg 25940

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 even needs not 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 26024). 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 e. _V |-> ran (iEdg ` g ) )

Detailed syntax breakdown of Definition df-edg

Step	Hyp	Ref	Expression
1		cedg 25939	. 2 class Edg
2		vg	. . 3 setvar g
3		cvv 3200	. . 3 class _V
4	2	cv 1482	. . . . 5 class g
5		ciedg 25875	. . . . 5 class iEdg
6	4, 5	cfv 5888	. . . 4 class (iEdg ` g )
7	6	crn 5115	. . 3 class ran (iEdg ` g )
8	2, 3, 7	cmpt 4729	. 2 class ( g e. _V |-> ran (iEdg ` g ) )
9	1, 8	wceq 1483	1 wff Edg = ( g e. _V |-> ran (iEdg ` g ) )

This definition is referenced by:  edgval  25941  edgvalOLD  25942