Definition df-re 15057

Description: Define a function whose value is the real part of a complex number. See reval 15063 for its value, recli 15124 for its closure, and replim 15073 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

Step	Hyp	Ref	Expression
1		cre 15054	. 2 class ℜ
2		vx	. . 3 setvar 𝑥
3		cc 11032	. . 3 class ℂ
4	2	cv 1547	. . . . 5 class 𝑥
5		ccj 15053	. . . . . 6 class ∗
6	4, 5	cfv 6488	. . . . 5 class (∗‘𝑥)
7		caddc 11037	. . . . 5 class +
8	4, 6, 7	co 7359	. . . 4 class (𝑥 + (∗‘𝑥))
9		c2 12231	. . . 4 class 2
10		cdiv 11803	. . . 4 class /
11	8, 9, 10	co 7359	. . 3 class ((𝑥 + (∗‘𝑥)) / 2)
12	2, 3, 11	cmpt 5155	. 2 class (𝑥 ∈ ℂ ↦ ((𝑥 + (∗‘𝑥)) / 2))
13	1, 12	wceq 1548	1 wff ℜ = (𝑥 ∈ ℂ ↦ ((𝑥 + (∗‘𝑥)) / 2))

This definition is referenced by:  reval  15063  ref  15069  cnre2csqima  34105