Definition df-im 10772

Description: Define a function whose value is the imaginary part of a complex number. See imval 10778 for its value, imcli 10840 for its closure, and replim 10787 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 10769	. 2 class Im
2		vx	. . 3 setvar x
3		cc 7742	. . 3 class CC
4	2	cv 1341	. . . . 5 class x
5		ci 7746	. . . . 5 class _i
6		cdiv 8559	. . . . 5 class /
7	4, 5, 6	co 5836	. . . 4 class ( x / _i )
8		cre 10768	. . . 4 class Re
9	7, 8	cfv 5182	. . 3 class ( Re ` ( x / _i ) )
10	2, 3, 9	cmpt 4037	. 2 class ( x e. CC |-> ( Re ` ( x / _i ) ) )
11	1, 10	wceq 1342	1 wff Im = ( x e. CC |-> ( Re ` ( x / _i ) ) )

This definition is referenced by:  imval  10778  imf  10784