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Definition df-re 11585
Description: Define a function whose value is the real part of a complex number. See reval 11591 for its value, recli 11652 for its closure, and replim 11601 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 11582 . 2  class  Re
2 vx . . 3  set  x
3 cc 8735 . . 3  class  CC
42cv 1622 . . . . 5  class  x
5 ccj 11581 . . . . . 6  class  *
64, 5cfv 5255 . . . . 5  class  ( * `
 x )
7 caddc 8740 . . . . 5  class  +
84, 6, 7co 5858 . . . 4  class  ( x  +  ( * `  x ) )
9 c2 9795 . . . 4  class  2
10 cdiv 9423 . . . 4  class  /
118, 9, 10co 5858 . . 3  class  ( ( x  +  ( * `
 x ) )  /  2 )
122, 3, 11cmpt 4077 . 2  class  ( x  e.  CC  |->  ( ( x  +  ( * `
 x ) )  /  2 ) )
131, 12wceq 1623 1  wff  Re  =  ( x  e.  CC  |->  ( ( x  +  ( * `  x
) )  /  2
) )
Colors of variables: wff set class
This definition is referenced by:  reval  11591  ref  11597  cnre2csqima  23295
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