Definition df-iedg 29404

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 29402	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3457	. . 3 class V
4	2	cv 1569	. . . . 5 class 𝑔
5	3, 3	cxp 5661	. . . . 5 class (V × V)
6	4, 5	wcel 2146	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7991	. . . . 5 class 2nd
8	4, 7	cfv 6540	. . . 4 class (2nd ‘𝑔)
9		cedgf 29393	. . . . 5 class .ef
10	4, 9	cfv 6540	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4489	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5194	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1570	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is used by:  iedgval  29406