Definition df-iedg 27414

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 27412	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3437	. . 3 class V
4	2	cv 1538	. . . . 5 class 𝑔
5	3, 3	cxp 5598	. . . . 5 class (V × V)
6	4, 5	wcel 2104	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7862	. . . . 5 class 2nd
8	4, 7	cfv 6458	. . . 4 class (2nd ‘𝑔)
9		cedgf 27401	. . . . 5 class .ef
10	4, 9	cfv 6458	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4465	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5164	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1539	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  27416