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Mirrors > Home > MPE Home > Th. List > df-im | Structured version Visualization version GIF version |
Description: Define a function whose value is the imaginary part of a complex number. See imval 13695 for its value, imcli 13756 for its closure, and replim 13704 for its use in decomposing a complex number. (Contributed by NM, 9-May-1999.) |
Ref | Expression |
---|---|
df-im | ⊢ ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i))) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cim 13686 | . 2 class ℑ | |
2 | vx | . . 3 setvar 𝑥 | |
3 | cc 9813 | . . 3 class ℂ | |
4 | 2 | cv 1474 | . . . . 5 class 𝑥 |
5 | ci 9817 | . . . . 5 class i | |
6 | cdiv 10563 | . . . . 5 class / | |
7 | 4, 5, 6 | co 6549 | . . . 4 class (𝑥 / i) |
8 | cre 13685 | . . . 4 class ℜ | |
9 | 7, 8 | cfv 5804 | . . 3 class (ℜ‘(𝑥 / i)) |
10 | 2, 3, 9 | cmpt 4643 | . 2 class (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i))) |
11 | 1, 10 | wceq 1475 | 1 wff ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i))) |
Colors of variables: wff setvar class |
This definition is referenced by: imval 13695 imf 13701 cnre2csqima 29285 |
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