Definition df-edg 16053

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 e. _V |-> ran (iEdg ` g ) )

Detailed syntax breakdown of Definition df-edg

Step	Hyp	Ref	Expression
1		cedg 16052	. 2 class Edg
2		vg	. . 3 setvar g
3		cvv 2813	. . 3 class _V
4	2	cv 1397	. . . . 5 class g
5		ciedg 16008	. . . . 5 class iEdg
6	4, 5	cfv 5352	. . . 4 class (iEdg ` g )
7	6	crn 4750	. . 3 class ran (iEdg ` g )
8	2, 3, 7	cmpt 4171	. 2 class ( g e. _V |-> ran (iEdg ` g ) )
9	1, 8	wceq 1398	1 wff Edg = ( g e. _V |-> ran (iEdg ` g ) )

This definition is referenced by:  edgvalg  16054  edgval  16055  edgopval  16057  edgstruct  16059