Definition df-iedg 29030

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 29028	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3477	. . 3 class V
4	2	cv 1535	. . . . 5 class 𝑔
5	3, 3	cxp 5686	. . . . 5 class (V × V)
6	4, 5	wcel 2105	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 8011	. . . . 5 class 2nd
8	4, 7	cfv 6562	. . . 4 class (2nd ‘𝑔)
9		cedgf 29017	. . . . 5 class .ef
10	4, 9	cfv 6562	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4530	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5230	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1536	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  29032