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Definition df-im 10648
Description: Define a function whose value is the imaginary part of a complex number. See imval 10654 for its value, imcli 10716 for its closure, and replim 10663 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 10645 . 2 class
2 vx . . 3 setvar 𝑥
3 cc 7642 . . 3 class
42cv 1331 . . . . 5 class 𝑥
5 ci 7646 . . . . 5 class i
6 cdiv 8456 . . . . 5 class /
74, 5, 6co 5782 . . . 4 class (𝑥 / i)
8 cre 10644 . . . 4 class
97, 8cfv 5131 . . 3 class (ℜ‘(𝑥 / i))
102, 3, 9cmpt 3997 . 2 class (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))
111, 10wceq 1332 1 wff ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))
Colors of variables: wff set class
This definition is referenced by:  imval  10654  imf  10660
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