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Definition df-im 9052
 Description: Define a function whose value is the imaginary part of a complex number. See imval 9058 for its value, imcli 9120 for its closure, and replim 9067 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 9049 . 2 class
2 vx . . 3 setvar x
3 cc 6689 . . 3 class
42cv 1241 . . . . 5 class x
5 ci 6693 . . . . 5 class i
6 cdiv 7413 . . . . 5 class /
74, 5, 6co 5455 . . . 4 class (x / i)
8 cre 9048 . . . 4 class
97, 8cfv 4845 . . 3 class (ℜ‘(x / i))
102, 3, 9cmpt 3809 . 2 class (x ℂ ↦ (ℜ‘(x / i)))
111, 10wceq 1242 1 wff ℑ = (x ℂ ↦ (ℜ‘(x / i)))
 Colors of variables: wff set class This definition is referenced by:  imval  9058  imf  9064
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