Definition df-iedg 26098

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 26096	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3351	. . 3 class V
4	2	cv 1630	. . . . 5 class 𝑔
5	3, 3	cxp 5248	. . . . 5 class (V × V)
6	4, 5	wcel 2145	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7318	. . . . 5 class 2nd
8	4, 7	cfv 6030	. . . 4 class (2nd ‘𝑔)
9		cedgf 26088	. . . . 5 class .ef
10	4, 9	cfv 6030	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4226	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 4864	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1631	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  26100  iedgvalOLD  26102