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Definition df-abs 15271
Description: Define the function for the absolute value (modulus) of a complex number. See abscli 15430 for its closure and absval 15273 or absval2i 15432 for its value. For example, (abs‘-2) = 2 (ex-abs 30483). (Contributed by NM, 27-Jul-1999.)
Assertion
Ref Expression
df-abs abs = (𝑥 ∈ ℂ ↦ (√‘(𝑥 · (∗‘𝑥))))

Detailed syntax breakdown of Definition df-abs
StepHypRef Expression
1 cabs 15269 . 2 class abs
2 vx . . 3 setvar 𝑥
3 cc 11150 . . 3 class
42cv 1535 . . . . 5 class 𝑥
5 ccj 15131 . . . . . 6 class
64, 5cfv 6562 . . . . 5 class (∗‘𝑥)
7 cmul 11157 . . . . 5 class ·
84, 6, 7co 7430 . . . 4 class (𝑥 · (∗‘𝑥))
9 csqrt 15268 . . . 4 class
108, 9cfv 6562 . . 3 class (√‘(𝑥 · (∗‘𝑥)))
112, 3, 10cmpt 5230 . 2 class (𝑥 ∈ ℂ ↦ (√‘(𝑥 · (∗‘𝑥))))
121, 11wceq 1536 1 wff abs = (𝑥 ∈ ℂ ↦ (√‘(𝑥 · (∗‘𝑥))))
Colors of variables: wff setvar class
This definition is referenced by:  absval  15273  absf  15372  absfico  45160
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