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Definition df-cj 9050
Description: Define the complex conjugate function. See cjcli 9121 for its closure and cjval 9053 for its value. (Contributed by NM, 9-May-1999.) (Revised by Mario Carneiro, 6-Nov-2013.)
Assertion
Ref Expression
df-cj ∗ = (x ℂ ↦ (y ℂ ((x + y) (i · (xy)) ℝ)))
Distinct variable group:   x,y

Detailed syntax breakdown of Definition df-cj
StepHypRef Expression
1 ccj 9047 . 2 class
2 vx . . 3 setvar x
3 cc 6689 . . 3 class
42cv 1241 . . . . . . 7 class x
5 vy . . . . . . . 8 setvar y
65cv 1241 . . . . . . 7 class y
7 caddc 6694 . . . . . . 7 class +
84, 6, 7co 5455 . . . . . 6 class (x + y)
9 cr 6690 . . . . . 6 class
108, 9wcel 1390 . . . . 5 wff (x + y)
11 ci 6693 . . . . . . 7 class i
12 cmin 6959 . . . . . . . 8 class
134, 6, 12co 5455 . . . . . . 7 class (xy)
14 cmul 6696 . . . . . . 7 class ·
1511, 13, 14co 5455 . . . . . 6 class (i · (xy))
1615, 9wcel 1390 . . . . 5 wff (i · (xy))
1710, 16wa 97 . . . 4 wff ((x + y) (i · (xy)) ℝ)
1817, 5, 3crio 5410 . . 3 class (y ℂ ((x + y) (i · (xy)) ℝ))
192, 3, 18cmpt 3809 . 2 class (x ℂ ↦ (y ℂ ((x + y) (i · (xy)) ℝ)))
201, 19wceq 1242 1 wff ∗ = (x ℂ ↦ (y ℂ ((x + y) (i · (xy)) ℝ)))
Colors of variables: wff set class
This definition is referenced by:  cjval  9053  cjf  9055
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