Definition df-iedg 29017

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 29015	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3479	. . 3 class V
4	2	cv 1538	. . . . 5 class 𝑔
5	3, 3	cxp 5682	. . . . 5 class (V × V)
6	4, 5	wcel 2107	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 8014	. . . . 5 class 2nd
8	4, 7	cfv 6560	. . . 4 class (2nd ‘𝑔)
9		cedgf 29004	. . . . 5 class .ef
10	4, 9	cfv 6560	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4524	. . 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 1539	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  29019