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Definition df-im 11676
Description: Define a function whose value is the imaginary part of a complex number. See imval 11682 for its value, imcli 11743 for its closure, and replim 11691 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
StepHypRef Expression
1 cim 11673 . 2  class  Im
2 vx . . 3  set  x
3 cc 8822 . . 3  class  CC
42cv 1641 . . . . 5  class  x
5 ci 8826 . . . . 5  class  _i
6 cdiv 9510 . . . . 5  class  /
74, 5, 6co 5942 . . . 4  class  ( x  /  _i )
8 cre 11672 . . . 4  class  Re
97, 8cfv 5334 . . 3  class  ( Re
`  ( x  /  _i ) )
102, 3, 9cmpt 4156 . 2  class  ( x  e.  CC  |->  ( Re
`  ( x  /  _i ) ) )
111, 10wceq 1642 1  wff  Im  =  ( x  e.  CC  |->  ( Re `  ( x  /  _i ) ) )
Colors of variables: wff set class
This definition is referenced by:  imval  11682  imf  11688  cnre2csqima  23465
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