Definition df-edg 15908

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 15907	. 2 class Edg
2		vg	. . 3 setvar g
3		cvv 2802	. . 3 class _V
4	2	cv 1396	. . . . 5 class g
5		ciedg 15863	. . . . 5 class iEdg
6	4, 5	cfv 5326	. . . 4 class (iEdg ` g )
7	6	crn 4726	. . 3 class ran (iEdg ` g )
8	2, 3, 7	cmpt 4150	. 2 class ( g e. _V |-> ran (iEdg ` g ) )
9	1, 8	wceq 1397	1 wff Edg = ( g e. _V |-> ran (iEdg ` g ) )

This definition is referenced by:  edgvalg  15909  edgval  15910  edgopval  15912  edgstruct  15914