Definition df-iedg 29634

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 29632	. 2 class iEdg
2		vg	. . 3 setvar 𝑔
3		cvv 3454	. . 3 class V
4	2	cv 1569	. . . . 5 class 𝑔
5	3, 3	cxp 5656	. . . . 5 class (V × V)
6	4, 5	wcel 2147	. . . 4 wff 𝑔 ∈ (V × V)
7		c2nd 8034	. . . . 5 class 2nd
8	4, 7	cfv 6566	. . . 4 class (2nd ‘𝑔)
9		cedgf 29623	. . . . 5 class .ef
10	4, 9	cfv 6566	. . . 4 class (.ef‘𝑔)
11	6, 8, 10	cif 4485	. . 3 class if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔))
12	2, 3, 11	cmpt 5192	. 2 class (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))
13	1, 12	wceq 1570	1 wff iEdg = (𝑔 ∈ V ↦ if(𝑔 ∈ (V × V), (2nd ‘𝑔), (.ef‘𝑔)))

This definition is used by:  iedgval  29636