Definition df-iedg 28983

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 28981	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3464	. . 3 class V
4	2	cv 1539	. . . . 5 class 𝑔
5	3, 3	cxp 5657	. . . . 5 class (V × V)
6	4, 5	wcel 2109	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7992	. . . . 5 class 2nd
8	4, 7	cfv 6536	. . . 4 class (2nd ‘𝑔)
9		cedgf 28972	. . . . 5 class .ef
10	4, 9	cfv 6536	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4505	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5206	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1540	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  28985