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Definition df-im 11581
Description: Define a function whose value is the imaginary part of a complex number. See imval 11587 for its value, imcli 11648 for its closure, and replim 11596 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 11578 . 2  class  Im
2 vx . . 3  set  x
3 cc 8731 . . 3  class  CC
42cv 1623 . . . . 5  class  x
5 ci 8735 . . . . 5  class  _i
6 cdiv 9419 . . . . 5  class  /
74, 5, 6co 5820 . . . 4  class  ( x  /  _i )
8 cre 11577 . . . 4  class  Re
97, 8cfv 5222 . . 3  class  ( Re
`  ( x  /  _i ) )
102, 3, 9cmpt 4079 . 2  class  ( x  e.  CC  |->  ( Re
`  ( x  /  _i ) ) )
111, 10wceq 1624 1  wff  Im  =  ( x  e.  CC  |->  ( Re `  ( x  /  _i ) ) )
Colors of variables: wff set class
This definition is referenced by:  imval  11587  imf  11593
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