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Definition df-abs 14685
Description: Define the function for the absolute value (modulus) of a complex number. See abscli 14845 for its closure and absval 14687 or absval2i 14847 for its value. For example, (abs‘-2) = 2 (ex-abs 28392). (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 14683 . 2 class abs
2 vx . . 3 setvar 𝑥
3 cc 10613 . . 3 class
42cv 1541 . . . . 5 class 𝑥
5 ccj 14545 . . . . . 6 class
64, 5cfv 6339 . . . . 5 class (∗‘𝑥)
7 cmul 10620 . . . . 5 class ·
84, 6, 7co 7170 . . . 4 class (𝑥 · (∗‘𝑥))
9 csqrt 14682 . . . 4 class
108, 9cfv 6339 . . 3 class (√‘(𝑥 · (∗‘𝑥)))
112, 3, 10cmpt 5110 . 2 class (𝑥 ∈ ℂ ↦ (√‘(𝑥 · (∗‘𝑥))))
121, 11wceq 1542 1 wff abs = (𝑥 ∈ ℂ ↦ (√‘(𝑥 · (∗‘𝑥))))
Colors of variables: wff setvar class
This definition is referenced by:  absval  14687  absf  14787  absfico  42296
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