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

Definition df-re 9443
Description: Define a function whose value is the real part of a complex number. See reval 9449 for its value, recli 9511 for its closure, and replim 9459 for its use in decomposing a complex number. (Contributed by NM, 9-May-1999.)
Assertion
Ref Expression
df-re ℜ = (𝑥 ∈ ℂ ↦ ((𝑥 + (∗‘𝑥)) / 2))

Detailed syntax breakdown of Definition df-re
StepHypRef Expression
1 cre 9440 . 2 class
2 vx . . 3 setvar 𝑥
3 cc 6887 . . 3 class
42cv 1242 . . . . 5 class 𝑥
5 ccj 9439 . . . . . 6 class
64, 5cfv 4902 . . . . 5 class (∗‘𝑥)
7 caddc 6892 . . . . 5 class +
84, 6, 7co 5512 . . . 4 class (𝑥 + (∗‘𝑥))
9 c2 7964 . . . 4 class 2
10 cdiv 7651 . . . 4 class /
118, 9, 10co 5512 . . 3 class ((𝑥 + (∗‘𝑥)) / 2)
122, 3, 11cmpt 3818 . 2 class (𝑥 ∈ ℂ ↦ ((𝑥 + (∗‘𝑥)) / 2))
131, 12wceq 1243 1 wff ℜ = (𝑥 ∈ ℂ ↦ ((𝑥 + (∗‘𝑥)) / 2))
Colors of variables: wff set class
This definition is referenced by:  reval  9449  ref  9455
  Copyright terms: Public domain W3C validator