Definition df-edg 16397

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 16396	. 2 class Edg
2		vg	. . 3 setvar g
3		cvv 2821	. . 3 class _V
4	2	cv 1401	. . . . 5 class g
5		ciedg 16352	. . . . 5 class iEdg
6	4, 5	cfv 5377	. . . 4 class (iEdg ` g )
7	6	crn 4775	. . 3 class ran (iEdg ` g )
8	2, 3, 7	cmpt 4192	. 2 class ( g e. _V |-> ran (iEdg ` g ) )
9	1, 8	wceq 1402	1 wff Edg = ( g e. _V |-> ran (iEdg ` g ) )

This definition is used by:  edgvalg  16398  edgval  16399  edgopval  16401  edgstruct  16403