Definition df-iedg 28926

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 28924	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3447	. . 3 class V
4	2	cv 1539	. . . . 5 class 𝑔
5	3, 3	cxp 5636	. . . . 5 class (V × V)
6	4, 5	wcel 2109	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7967	. . . . 5 class 2nd
8	4, 7	cfv 6511	. . . 4 class (2nd ‘𝑔)
9		cedgf 28915	. . . . 5 class .ef
10	4, 9	cfv 6511	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4488	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5188	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1540	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  28928