MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-im Unicode version

Definition df-im 11586
Description: Define a function whose value is the imaginary part of a complex number. See imval 11592 for its value, imcli 11653 for its closure, and replim 11601 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 11583 . 2  class  Im
2 vx . . 3  set  x
3 cc 8735 . . 3  class  CC
42cv 1622 . . . . 5  class  x
5 ci 8739 . . . . 5  class  _i
6 cdiv 9423 . . . . 5  class  /
74, 5, 6co 5858 . . . 4  class  ( x  /  _i )
8 cre 11582 . . . 4  class  Re
97, 8cfv 5255 . . 3  class  ( Re
`  ( x  /  _i ) )
102, 3, 9cmpt 4077 . 2  class  ( x  e.  CC  |->  ( Re
`  ( x  /  _i ) ) )
111, 10wceq 1623 1  wff  Im  =  ( x  e.  CC  |->  ( Re `  ( x  /  _i ) ) )
Colors of variables: wff set class
This definition is referenced by:  imval  11592  imf  11598  cnre2csqima  23295
  Copyright terms: Public domain W3C validator