Definition df-iedg 26792

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 26790	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3441	. . 3 class V
4	2	cv 1537	. . . . 5 class 𝑔
5	3, 3	cxp 5517	. . . . 5 class (V × V)
6	4, 5	wcel 2111	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 7670	. . . . 5 class 2nd
8	4, 7	cfv 6324	. . . 4 class (2nd ‘𝑔)
9		cedgf 26782	. . . . 5 class .ef
10	4, 9	cfv 6324	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4425	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5110	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1538	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is referenced by:  iedgval  26794