Definition df-iedg 29084

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 29082	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3442	. . 3 class V
4	2	cv 1541	. . . . 5 class 𝑔
5	3, 3	cxp 5630	. . . . 5 class (V × V)
6	4, 5	wcel 2114	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7942	. . . . 5 class 2nd
8	4, 7	cfv 6500	. . . 4 class (2nd ‘𝑔)
9		cedgf 29073	. . . . 5 class .ef
10	4, 9	cfv 6500	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4481	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5181	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1542	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  29086