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Definition df-re 10172
Description: Define a function whose value is the real part of a complex number. See reval 10178 for its value, recli 10240 for its closure, and replim 10188 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 10169 . 2  class  Re
2 vx . . 3  setvar  x
3 cc 7292 . . 3  class  CC
42cv 1286 . . . . 5  class  x
5 ccj 10168 . . . . . 6  class  *
64, 5cfv 4981 . . . . 5  class  ( * `
 x )
7 caddc 7297 . . . . 5  class  +
84, 6, 7co 5613 . . . 4  class  ( x  +  ( * `  x ) )
9 c2 8407 . . . 4  class  2
10 cdiv 8078 . . . 4  class  /
118, 9, 10co 5613 . . 3  class  ( ( x  +  ( * `
 x ) )  /  2 )
122, 3, 11cmpt 3874 . 2  class  ( x  e.  CC  |->  ( ( x  +  ( * `
 x ) )  /  2 ) )
131, 12wceq 1287 1  wff  Re  =  ( x  e.  CC  |->  ( ( x  +  ( * `  x
) )  /  2
) )
Colors of variables: wff set class
This definition is referenced by:  reval  10178  ref  10184
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