Definition df-iedg 28805

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 28803	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3469	. . 3 class V
4	2	cv 1533	. . . . 5 class 𝑔
5	3, 3	cxp 5670	. . . . 5 class (V × V)
6	4, 5	wcel 2099	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7986	. . . . 5 class 2nd
8	4, 7	cfv 6542	. . . 4 class (2nd ‘𝑔)
9		cedgf 28792	. . . . 5 class .ef
10	4, 9	cfv 6542	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4524	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5225	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1534	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  28807