ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-abs GIF version

Definition df-abs 10023
Description: Define the function for the absolute value (modulus) of a complex number. (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 10021 . 2 class abs
2 vx . . 3 setvar 𝑥
3 cc 7041 . . 3 class
42cv 1284 . . . . 5 class 𝑥
5 ccj 9864 . . . . . 6 class
64, 5cfv 4932 . . . . 5 class (∗‘𝑥)
7 cmul 7048 . . . . 5 class ·
84, 6, 7co 5543 . . . 4 class (𝑥 · (∗‘𝑥))
9 csqrt 10020 . . . 4 class
108, 9cfv 4932 . . 3 class (√‘(𝑥 · (∗‘𝑥)))
112, 3, 10cmpt 3847 . 2 class (𝑥 ∈ ℂ ↦ (√‘(𝑥 · (∗‘𝑥))))
121, 11wceq 1285 1 wff abs = (𝑥 ∈ ℂ ↦ (√‘(𝑥 · (∗‘𝑥))))
Colors of variables: wff set class
This definition is referenced by:  absval  10025  absf  10134
  Copyright terms: Public domain W3C validator