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Definition df-re 9051
Description: Define a function whose value is the real part of a complex number. See reval 9057 for its value, recli 9119 for its closure, and replim 9067 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 9048 . 2 class
2 vx . . 3 setvar x
3 cc 6689 . . 3 class
42cv 1241 . . . . 5 class x
5 ccj 9047 . . . . . 6 class
64, 5cfv 4845 . . . . 5 class (∗‘x)
7 caddc 6694 . . . . 5 class +
84, 6, 7co 5455 . . . 4 class (x + (∗‘x))
9 c2 7724 . . . 4 class 2
10 cdiv 7413 . . . 4 class /
118, 9, 10co 5455 . . 3 class ((x + (∗‘x)) / 2)
122, 3, 11cmpt 3809 . 2 class (x ℂ ↦ ((x + (∗‘x)) / 2))
131, 12wceq 1242 1 wff ℜ = (x ℂ ↦ ((x + (∗‘x)) / 2))
Colors of variables: wff set class
This definition is referenced by:  reval  9057  ref  9063
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