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

Definition df-re 11860
Description: Define a function whose value is the real part of a complex number. See reval 11866 for its value, recli 11927 for its closure, and replim 11876 for its use in decomposing a complex number. (Contributed by NM, 9-May-1999.)
Assertion
Ref Expression
df-re  |-  Re  =  ( x  e.  CC  |->  ( ( x  +  ( * `  x
) )  /  2
) )

Detailed syntax breakdown of Definition df-re
StepHypRef Expression
1 cre 11857 . 2  class  Re
2 vx . . 3  set  x
3 cc 8944 . . 3  class  CC
42cv 1648 . . . . 5  class  x
5 ccj 11856 . . . . . 6  class  *
64, 5cfv 5413 . . . . 5  class  ( * `
 x )
7 caddc 8949 . . . . 5  class  +
84, 6, 7co 6040 . . . 4  class  ( x  +  ( * `  x ) )
9 c2 10005 . . . 4  class  2
10 cdiv 9633 . . . 4  class  /
118, 9, 10co 6040 . . 3  class  ( ( x  +  ( * `
 x ) )  /  2 )
122, 3, 11cmpt 4226 . 2  class  ( x  e.  CC  |->  ( ( x  +  ( * `
 x ) )  /  2 ) )
131, 12wceq 1649 1  wff  Re  =  ( x  e.  CC  |->  ( ( x  +  ( * `  x
) )  /  2
) )
Colors of variables: wff set class
This definition is referenced by:  reval  11866  ref  11872  cnre2csqima  24262
  Copyright terms: Public domain W3C validator