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Definition df-abs 15180
Description: Define the function for the absolute value (modulus) of a complex number. See abscli 15339 for its closure and absval 15182 or absval2i 15341 for its value. For example, (abs‘-2) = 2 (ex-abs 30177). (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 15178 . 2 class abs
2 vx . . 3 setvar 𝑥
3 cc 11104 . . 3 class
42cv 1532 . . . . 5 class 𝑥
5 ccj 15040 . . . . . 6 class
64, 5cfv 6533 . . . . 5 class (∗‘𝑥)
7 cmul 11111 . . . . 5 class ·
84, 6, 7co 7401 . . . 4 class (𝑥 · (∗‘𝑥))
9 csqrt 15177 . . . 4 class
108, 9cfv 6533 . . 3 class (√‘(𝑥 · (∗‘𝑥)))
112, 3, 10cmpt 5221 . 2 class (𝑥 ∈ ℂ ↦ (√‘(𝑥 · (∗‘𝑥))))
121, 11wceq 1533 1 wff abs = (𝑥 ∈ ℂ ↦ (√‘(𝑥 · (∗‘𝑥))))
Colors of variables: wff setvar class
This definition is referenced by:  absval  15182  absf  15281  absfico  44402
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