Definition df-iedg 29289

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 29287	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3463	. . 3 class V
4	2	cv 1566	. . . . 5 class 𝑔
5	3, 3	cxp 5660	. . . . 5 class (V × V)
6	4, 5	wcel 2149	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7984	. . . . 5 class 2nd
8	4, 7	cfv 6537	. . . 4 class (2nd ‘𝑔)
9		cedgf 29278	. . . . 5 class .ef
10	4, 9	cfv 6537	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4492	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5196	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1567	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  29291