Definition df-iedg 15939

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 15937	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 2803	. . 3 class V
4	2	cv 1397	. . . . 5 class 𝑔
5	3, 3	cxp 4729	. . . . 5 class (V × V)
6	4, 5	wcel 2202	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 6311	. . . . 5 class 2nd
8	4, 7	cfv 5333	. . . 4 class (2nd ‘𝑔)
9		cedgf 15928	. . . . 5 class .ef
10	4, 9	cfv 5333	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 3607	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 4155	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1398	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgvalg  15941  edgval  15984