Definition df-iedg 29586

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 29584	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3450	. . 3 class V
4	2	cv 1568	. . . . 5 class 𝑔
5	3, 3	cxp 5649	. . . . 5 class (V × V)
6	4, 5	wcel 2144	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 8004	. . . . 5 class 2nd
8	4, 7	cfv 6543	. . . 4 class (2nd ‘𝑔)
9		cedgf 29575	. . . . 5 class .ef
10	4, 9	cfv 6543	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4481	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5185	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1569	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is used by:  iedgval  29588