Definition df-iedg 29349

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 29347	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3455	. . 3 class V
4	2	cv 1569	. . . . 5 class 𝑔
5	3, 3	cxp 5659	. . . . 5 class (V × V)
6	4, 5	wcel 2143	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7981	. . . . 5 class 2nd
8	4, 7	cfv 6536	. . . 4 class (2nd ‘𝑔)
9		cedgf 29338	. . . . 5 class .ef
10	4, 9	cfv 6536	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4487	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5192	. 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 referenced by:  iedgval  29351