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

Definition df-re 9671
Description: Define a function whose value is the real part of a complex number. See reval 9677 for its value, recli 9739 for its closure, and replim 9687 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 9668 . 2  class  Re
2 vx . . 3  setvar  x
3 cc 6945 . . 3  class  CC
42cv 1258 . . . . 5  class  x
5 ccj 9667 . . . . . 6  class  *
64, 5cfv 4930 . . . . 5  class  ( * `
 x )
7 caddc 6950 . . . . 5  class  +
84, 6, 7co 5540 . . . 4  class  ( x  +  ( * `  x ) )
9 c2 8040 . . . 4  class  2
10 cdiv 7725 . . . 4  class  /
118, 9, 10co 5540 . . 3  class  ( ( x  +  ( * `
 x ) )  /  2 )
122, 3, 11cmpt 3846 . 2  class  ( x  e.  CC  |->  ( ( x  +  ( * `
 x ) )  /  2 ) )
131, 12wceq 1259 1  wff  Re  =  ( x  e.  CC  |->  ( ( x  +  ( * `  x
) )  /  2
) )
Colors of variables: wff set class
This definition is referenced by:  reval  9677  ref  9683
  Copyright terms: Public domain W3C validator