Definition df-iedg 29034

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 29032	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3488	. . 3 class V
4	2	cv 1536	. . . . 5 class 𝑔
5	3, 3	cxp 5698	. . . . 5 class (V × V)
6	4, 5	wcel 2108	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 8029	. . . . 5 class 2nd
8	4, 7	cfv 6573	. . . 4 class (2nd ‘𝑔)
9		cedgf 29021	. . . . 5 class .ef
10	4, 9	cfv 6573	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4548	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5249	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1537	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  29036