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Definition df-cj 6684
Description: Define the complex conjugate function. See cjcl 6699 for its closure and cjvalt 6695 for its value.
Assertion
Ref Expression
df-cj |- * = {<.x, y>. | (x e. CC /\ y = ((Re` x) - (i x. (Im` x))))}
Distinct variable group:   x,y

Detailed syntax breakdown of Definition df-cj
StepHypRef Expression
1 ccj 6680 . 2 class *
2 vx . . . . . 6 set x
32cv 952 . . . . 5 class x
4 cc 5204 . . . . 5 class CC
53, 4wcel 955 . . . 4 wff x e. CC
6 vy . . . . . 6 set y
76cv 952 . . . . 5 class y
8 cre 6678 . . . . . . 7 class Re
93, 8cfv 3172 . . . . . 6 class (Re` x)
10 ci 5208 . . . . . . 7 class i
11 cim 6679 . . . . . . . 8 class Im
123, 11cfv 3172 . . . . . . 7 class (Im` x)
13 cmul 5211 . . . . . . 7 class x.
1410, 12, 13co 3948 . . . . . 6 class (i x. (Im` x))
15 cmin 5264 . . . . . 6 class -
169, 14, 15co 3948 . . . . 5 class ((Re` x) - (i x. (Im` x)))
177, 16wceq 953 . . . 4 wff y = ((Re` x) - (i x. (Im` x)))
185, 17wa 223 . . 3 wff (x e. CC /\ y = ((Re` x) - (i x. (Im` x))))
1918, 2, 6copab 2656 . 2 class {<.x, y>. | (x e. CC /\ y = ((Re` x) - (i x. (Im` x))))}
201, 19wceq 953 1 wff * = {<.x, y>. | (x e. CC /\ y = ((Re` x) - (i x. (Im` x))))}
Colors of variables: wff set class
This definition is referenced by:  cjvalt 6695  cjcncf 7213
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