Definition df-iedg 29086

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 29084	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3431	. . 3 class V
4	2	cv 1546	. . . . 5 class 𝑔
5	3, 3	cxp 5616	. . . . 5 class (V × V)
6	4, 5	wcel 2119	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7930	. . . . 5 class 2nd
8	4, 7	cfv 6485	. . . 4 class (2nd ‘𝑔)
9		cedgf 29075	. . . . 5 class .ef
10	4, 9	cfv 6485	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4454	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5153	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1547	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  29088