Definition df-iedg 29068

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 29066	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3429	. . 3 class V
4	2	cv 1541	. . . . 5 class 𝑔
5	3, 3	cxp 5629	. . . . 5 class (V × V)
6	4, 5	wcel 2114	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7941	. . . . 5 class 2nd
8	4, 7	cfv 6498	. . . 4 class (2nd ‘𝑔)
9		cedgf 29057	. . . . 5 class .ef
10	4, 9	cfv 6498	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4466	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5166	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1542	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  29070