Definition df-iedg 15556

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 15554	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 2771	. . 3 class V
4	2	cv 1371	. . . . 5 class 𝑔
5	3, 3	cxp 4672	. . . . 5 class (V × V)
6	4, 5	wcel 2175	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 6224	. . . . 5 class 2nd
8	4, 7	cfv 5270	. . . 4 class (2nd ‘𝑔)
9		cedgf 15545	. . . . 5 class .ef
10	4, 9	cfv 5270	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 3570	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 4104	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1372	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgvalg  15558