Definition df-iedg 28902

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 28900	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3444	. . 3 class V
4	2	cv 1539	. . . . 5 class 𝑔
5	3, 3	cxp 5629	. . . . 5 class (V × V)
6	4, 5	wcel 2109	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7946	. . . . 5 class 2nd
8	4, 7	cfv 6499	. . . 4 class (2nd ‘𝑔)
9		cedgf 28891	. . . . 5 class .ef
10	4, 9	cfv 6499	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4484	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5183	. 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  28904