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Definition df-im 13631
Description: Define a function whose value is the imaginary part of a complex number. See imval 13637 for its value, imcli 13698 for its closure, and replim 13646 for its use in decomposing a complex number. (Contributed by NM, 9-May-1999.)
Assertion
Ref Expression
df-im ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))

Detailed syntax breakdown of Definition df-im
StepHypRef Expression
1 cim 13628 . 2 class
2 vx . . 3 setvar 𝑥
3 cc 9786 . . 3 class
42cv 1473 . . . . 5 class 𝑥
5 ci 9790 . . . . 5 class i
6 cdiv 10529 . . . . 5 class /
74, 5, 6co 6523 . . . 4 class (𝑥 / i)
8 cre 13627 . . . 4 class
97, 8cfv 5786 . . 3 class (ℜ‘(𝑥 / i))
102, 3, 9cmpt 4633 . 2 class (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))
111, 10wceq 1474 1 wff ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))
Colors of variables: wff setvar class
This definition is referenced by:  imval  13637  imf  13643  cnre2csqima  29087
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