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Definition df-im 10173
Description: Define a function whose value is the imaginary part of a complex number. See imval 10179 for its value, imcli 10241 for its closure, and replim 10188 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 10170 . 2 class
2 vx . . 3 setvar 𝑥
3 cc 7292 . . 3 class
42cv 1286 . . . . 5 class 𝑥
5 ci 7296 . . . . 5 class i
6 cdiv 8078 . . . . 5 class /
74, 5, 6co 5613 . . . 4 class (𝑥 / i)
8 cre 10169 . . . 4 class
97, 8cfv 4981 . . 3 class (ℜ‘(𝑥 / i))
102, 3, 9cmpt 3874 . 2 class (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))
111, 10wceq 1287 1 wff ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))
Colors of variables: wff set class
This definition is referenced by:  imval  10179  imf  10185
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