Definition df-iedg 15865

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 15863	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 2802	. . 3 class V
4	2	cv 1396	. . . . 5 class 𝑔
5	3, 3	cxp 4723	. . . . 5 class (V × V)
6	4, 5	wcel 2202	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 6301	. . . . 5 class 2nd
8	4, 7	cfv 5326	. . . 4 class (2nd ‘𝑔)
9		cedgf 15854	. . . . 5 class .ef
10	4, 9	cfv 5326	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 3605	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 4150	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1397	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgvalg  15867  edgval  15910