Definition df-iedg 28832

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 28830	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3473	. . 3 class V
4	2	cv 1532	. . . . 5 class 𝑔
5	3, 3	cxp 5680	. . . . 5 class (V × V)
6	4, 5	wcel 2098	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7998	. . . . 5 class 2nd
8	4, 7	cfv 6553	. . . 4 class (2nd ‘𝑔)
9		cedgf 28819	. . . . 5 class .ef
10	4, 9	cfv 6553	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4532	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5235	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1533	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  28834