Definition df-iedg 15831

Description: Define the function mapping a graph to its indexed edges. This definition is very general: It defines the indexed edges for any ordered pair as its second component, and for any other class as its "edge function". It is meaningful, however, only if the ordered pair represents a graph resp. the class is an extensible structure (containing a slot for "edge functions") representing a graph. (Contributed by AV, 20-Sep-2020.)

Assertion

Ref	Expression
df-iedg	⊢ iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

Detailed syntax breakdown of Definition df-iedg

Step	Hyp	Ref	Expression
1		ciedg 15829	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 2799	. . 3 class V
4	2	cv 1394	. . . . 5 class 𝑔
5	3, 3	cxp 4717	. . . . 5 class (V × V)
6	4, 5	wcel 2200	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 6291	. . . . 5 class 2nd
8	4, 7	cfv 5318	. . . 4 class (2nd ‘𝑔)
9		cedgf 15820	. . . . 5 class .ef
10	4, 9	cfv 5318	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 3602	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 4145	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1395	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgvalg  15833