ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-im Unicode version

Definition df-im 10647
Description: Define a function whose value is the imaginary part of a complex number. See imval 10653 for its value, imcli 10715 for its closure, and replim 10662 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 10644 . 2  class  Im
2 vx . . 3  setvar  x
3 cc 7641 . . 3  class  CC
42cv 1331 . . . . 5  class  x
5 ci 7645 . . . . 5  class  _i
6 cdiv 8455 . . . . 5  class  /
74, 5, 6co 5781 . . . 4  class  ( x  /  _i )
8 cre 10643 . . . 4  class  Re
97, 8cfv 5130 . . 3  class  ( Re
`  ( x  /  _i ) )
102, 3, 9cmpt 3996 . 2  class  ( x  e.  CC  |->  ( Re
`  ( x  /  _i ) ) )
111, 10wceq 1332 1  wff  Im  =  ( x  e.  CC  |->  ( Re `  ( x  /  _i ) ) )
Colors of variables: wff set class
This definition is referenced by:  imval  10653  imf  10659
  Copyright terms: Public domain W3C validator