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Definition df-abs 12161
Description: Define the function for the absolute value (modulus) of a complex number. See abscli 12318 for its closure and absval 12163 or absval2i 12320 for its value. (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 12159 . 2 class abs
2 vx . . 3 set 𝑥
3 cc 9085 . . 3 class
42cv 1661 . . . . 5 class 𝑥
5 ccj 12021 . . . . . 6 class
64, 5cfv 5553 . . . . 5 class (∗‘𝑥)
7 cmul 9092 . . . . 5 class ·
84, 6, 7co 6181 . . . 4 class (𝑥 · (∗‘𝑥))
9 csqr 12158 . . . 4 class
108, 9cfv 5553 . . 3 class (√‘(𝑥 · (∗‘𝑥)))
112, 3, 10cmpt 4351 . 2 class (𝑥 ∈ ℂ ↦ (√‘(𝑥 · (∗‘𝑥))))
121, 11wceq 1662 1 wff abs = (𝑥 ∈ ℂ ↦ (√‘(𝑥 · (∗‘𝑥))))
Colors of variables: wff set class
This definition is referenced by:  absval  12163  absf  12261
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