Definition df-iedg 16010

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 16008	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 2813	. . 3 class V
4	2	cv 1397	. . . . 5 class 𝑔
5	3, 3	cxp 4747	. . . . 5 class (V × V)
6	4, 5	wcel 2203	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 6333	. . . . 5 class 2nd
8	4, 7	cfv 5352	. . . 4 class (2nd ‘𝑔)
9		cedgf 15999	. . . . 5 class .ef
10	4, 9	cfv 5352	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 3620	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 4171	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1398	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgvalg  16012  edgval  16055