Definition df-iedg 15689

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 15687	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 2773	. . 3 class V
4	2	cv 1372	. . . . 5 class 𝑔
5	3, 3	cxp 4681	. . . . 5 class (V × V)
6	4, 5	wcel 2177	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 6238	. . . . 5 class 2nd
8	4, 7	cfv 5280	. . . 4 class (2nd ‘𝑔)
9		cedgf 15678	. . . . 5 class .ef
10	4, 9	cfv 5280	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 3575	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 4113	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1373	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgvalg  15691