Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-im GIF version

Definition df-im 9869
 Description: Define a function whose value is the imaginary part of a complex number. See imval 9875 for its value, imcli 9937 for its closure, and replim 9884 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 9866 . 2 class
2 vx . . 3 setvar 𝑥
3 cc 7041 . . 3 class
42cv 1284 . . . . 5 class 𝑥
5 ci 7045 . . . . 5 class i
6 cdiv 7827 . . . . 5 class /
74, 5, 6co 5543 . . . 4 class (𝑥 / i)
8 cre 9865 . . . 4 class
97, 8cfv 4932 . . 3 class (ℜ‘(𝑥 / i))
102, 3, 9cmpt 3847 . 2 class (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))
111, 10wceq 1285 1 wff ℑ = (𝑥 ∈ ℂ ↦ (ℜ‘(𝑥 / i)))
 Colors of variables: wff set class This definition is referenced by:  imval  9875  imf  9881
 Copyright terms: Public domain W3C validator