Definition df-iedg 28256

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 28254	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3474	. . 3 class V
4	2	cv 1540	. . . . 5 class 𝑔
5	3, 3	cxp 5674	. . . . 5 class (V × V)
6	4, 5	wcel 2106	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7973	. . . . 5 class 2nd
8	4, 7	cfv 6543	. . . 4 class (2nd ‘𝑔)
9		cedgf 28243	. . . . 5 class .ef
10	4, 9	cfv 6543	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4528	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5231	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1541	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  28258