Definition df-iedg 28762

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 28760	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3468	. . 3 class V
4	2	cv 1532	. . . . 5 class 𝑔
5	3, 3	cxp 5667	. . . . 5 class (V × V)
6	4, 5	wcel 2098	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7970	. . . . 5 class 2nd
8	4, 7	cfv 6536	. . . 4 class (2nd ‘𝑔)
9		cedgf 28749	. . . . 5 class .ef
10	4, 9	cfv 6536	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4523	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5224	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1533	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  28764