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Definition df-re 11864
Description: Define a function whose value is the real part of a complex number. See reval 11870 for its value, recli 11931 for its closure, and replim 11880 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 11861 . 2  class  Re
2 vx . . 3  set  x
3 cc 8948 . . 3  class  CC
42cv 1648 . . . . 5  class  x
5 ccj 11860 . . . . . 6  class  *
64, 5cfv 5417 . . . . 5  class  ( * `
 x )
7 caddc 8953 . . . . 5  class  +
84, 6, 7co 6044 . . . 4  class  ( x  +  ( * `  x ) )
9 c2 10009 . . . 4  class  2
10 cdiv 9637 . . . 4  class  /
118, 9, 10co 6044 . . 3  class  ( ( x  +  ( * `
 x ) )  /  2 )
122, 3, 11cmpt 4230 . 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  11870  ref  11876  cnre2csqima  24266
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