Definition df-iedg 29072

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 29070	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3440	. . 3 class V
4	2	cv 1540	. . . . 5 class 𝑔
5	3, 3	cxp 5622	. . . . 5 class (V × V)
6	4, 5	wcel 2113	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7932	. . . . 5 class 2nd
8	4, 7	cfv 6492	. . . 4 class (2nd ‘𝑔)
9		cedgf 29061	. . . . 5 class .ef
10	4, 9	cfv 6492	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4479	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5179	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1541	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  29074