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Definition df-cj 10171
Description: Define the complex conjugate function. See cjcli 10242 for its closure and cjval 10174 for its value. (Contributed by NM, 9-May-1999.) (Revised by Mario Carneiro, 6-Nov-2013.)
Assertion
Ref Expression
df-cj  |-  *  =  ( x  e.  CC  |->  ( iota_ y  e.  CC  ( ( x  +  y )  e.  RR  /\  ( _i  x.  (
x  -  y ) )  e.  RR ) ) )
Distinct variable group:    x, y

Detailed syntax breakdown of Definition df-cj
StepHypRef Expression
1 ccj 10168 . 2  class  *
2 vx . . 3  setvar  x
3 cc 7292 . . 3  class  CC
42cv 1286 . . . . . . 7  class  x
5 vy . . . . . . . 8  setvar  y
65cv 1286 . . . . . . 7  class  y
7 caddc 7297 . . . . . . 7  class  +
84, 6, 7co 5613 . . . . . 6  class  ( x  +  y )
9 cr 7293 . . . . . 6  class  RR
108, 9wcel 1436 . . . . 5  wff  ( x  +  y )  e.  RR
11 ci 7296 . . . . . . 7  class  _i
12 cmin 7597 . . . . . . . 8  class  -
134, 6, 12co 5613 . . . . . . 7  class  ( x  -  y )
14 cmul 7299 . . . . . . 7  class  x.
1511, 13, 14co 5613 . . . . . 6  class  ( _i  x.  ( x  -  y ) )
1615, 9wcel 1436 . . . . 5  wff  ( _i  x.  ( x  -  y ) )  e.  RR
1710, 16wa 102 . . . 4  wff  ( ( x  +  y )  e.  RR  /\  (
_i  x.  ( x  -  y ) )  e.  RR )
1817, 5, 3crio 5568 . . 3  class  ( iota_ y  e.  CC  ( ( x  +  y )  e.  RR  /\  (
_i  x.  ( x  -  y ) )  e.  RR ) )
192, 3, 18cmpt 3874 . 2  class  ( x  e.  CC  |->  ( iota_ y  e.  CC  ( ( x  +  y )  e.  RR  /\  (
_i  x.  ( x  -  y ) )  e.  RR ) ) )
201, 19wceq 1287 1  wff  *  =  ( x  e.  CC  |->  ( iota_ y  e.  CC  ( ( x  +  y )  e.  RR  /\  ( _i  x.  (
x  -  y ) )  e.  RR ) ) )
Colors of variables: wff set class
This definition is referenced by:  cjval  10174  cjf  10176
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