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Definition df-cj 11584
Description: Define the complex conjugate function. See cjcli 11654 for its closure and cjval 11587 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 11581 . 2  class  *
2 vx . . 3  set  x
3 cc 8735 . . 3  class  CC
42cv 1622 . . . . . . 7  class  x
5 vy . . . . . . . 8  set  y
65cv 1622 . . . . . . 7  class  y
7 caddc 8740 . . . . . . 7  class  +
84, 6, 7co 5858 . . . . . 6  class  ( x  +  y )
9 cr 8736 . . . . . 6  class  RR
108, 9wcel 1684 . . . . 5  wff  ( x  +  y )  e.  RR
11 ci 8739 . . . . . . 7  class  _i
12 cmin 9037 . . . . . . . 8  class  -
134, 6, 12co 5858 . . . . . . 7  class  ( x  -  y )
14 cmul 8742 . . . . . . 7  class  x.
1511, 13, 14co 5858 . . . . . 6  class  ( _i  x.  ( x  -  y ) )
1615, 9wcel 1684 . . . . 5  wff  ( _i  x.  ( x  -  y ) )  e.  RR
1710, 16wa 358 . . . 4  wff  ( ( x  +  y )  e.  RR  /\  (
_i  x.  ( x  -  y ) )  e.  RR )
1817, 5, 3crio 6297 . . 3  class  ( iota_ y  e.  CC ( ( x  +  y )  e.  RR  /\  (
_i  x.  ( x  -  y ) )  e.  RR ) )
192, 3, 18cmpt 4077 . 2  class  ( x  e.  CC  |->  ( iota_ y  e.  CC ( ( x  +  y )  e.  RR  /\  (
_i  x.  ( x  -  y ) )  e.  RR ) ) )
201, 19wceq 1623 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  11587  cjf  11589
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