Definition df-iedg 15856

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 15854	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 2800	. . 3 class V
4	2	cv 1394	. . . . 5 class 𝑔
5	3, 3	cxp 4721	. . . . 5 class (V × V)
6	4, 5	wcel 2200	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 6297	. . . . 5 class 2nd
8	4, 7	cfv 5324	. . . 4 class (2nd ‘𝑔)
9		cedgf 15845	. . . . 5 class .ef
10	4, 9	cfv 5324	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 3603	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 4148	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1395	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgvalg  15858  edgval  15901