Definition df-im 9731

Description: Define a function whose value is the imaginary part of a complex number. See imval 9737 for its value, imcli 9799 for its closure, and replim 9746 for its use in decomposing a complex number. (Contributed by NM, 9-May-1999.)

Assertion

Ref	Expression
df-im	|- Im = ( x e. CC |-> ( Re ` ( x / _i ) ) )

Detailed syntax breakdown of Definition df-im

Step	Hyp	Ref	Expression
1		cim 9728	. 2 class Im
2		vx	. . 3 setvar x
3		cc 6979	. . 3 class CC
4	2	cv 1283	. . . . 5 class x
5		ci 6983	. . . . 5 class _i
6		cdiv 7760	. . . . 5 class /
7	4, 5, 6	co 5532	. . . 4 class ( x / _i )
8		cre 9727	. . . 4 class Re
9	7, 8	cfv 4922	. . 3 class ( Re ` ( x / _i ) )
10	2, 3, 9	cmpt 3839	. 2 class ( x e. CC |-> ( Re ` ( x / _i ) ) )
11	1, 10	wceq 1284	1 wff Im = ( x e. CC |-> ( Re ` ( x / _i ) ) )

This definition is referenced by:  imval  9737  imf  9743