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Definition df-re 13834
Description: Define a function whose value is the real part of a complex number. See reval 13840 for its value, recli 13901 for its closure, and replim 13850 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 13831 . 2 class
2 vx . . 3 setvar 𝑥
3 cc 9931 . . 3 class
42cv 1481 . . . . 5 class 𝑥
5 ccj 13830 . . . . . 6 class
64, 5cfv 5886 . . . . 5 class (∗‘𝑥)
7 caddc 9936 . . . . 5 class +
84, 6, 7co 6647 . . . 4 class (𝑥 + (∗‘𝑥))
9 c2 11067 . . . 4 class 2
10 cdiv 10681 . . . 4 class /
118, 9, 10co 6647 . . 3 class ((𝑥 + (∗‘𝑥)) / 2)
122, 3, 11cmpt 4727 . 2 class (𝑥 ∈ ℂ ↦ ((𝑥 + (∗‘𝑥)) / 2))
131, 12wceq 1482 1 wff ℜ = (𝑥 ∈ ℂ ↦ ((𝑥 + (∗‘𝑥)) / 2))
Colors of variables: wff setvar class
This definition is referenced by:  reval  13840  ref  13846  cnre2csqima  29942
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