Definition df-iedg 26351

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 26349	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3398	. . 3 class V
4	2	cv 1600	. . . . 5 class 𝑔
5	3, 3	cxp 5355	. . . . 5 class (V × V)
6	4, 5	wcel 2107	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7446	. . . . 5 class 2nd
8	4, 7	cfv 6137	. . . 4 class (2nd ‘𝑔)
9		cedgf 26341	. . . . 5 class .ef
10	4, 9	cfv 6137	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4307	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 4967	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1601	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  26353