Definition df-bj-inftyexpi 32271

Description: Definition of the auxiliary function inftyexpi parameterizing the circle at infinity ℂ_∞ in ℂ̅. We use coupling with ℂ to simplify the proof of bj-ccinftydisj 32277. It could seem more natural to define inftyexpi on all of ℝ using prcpal but we want to use only basic functions in the definition of ℂ̅. (Contributed by BJ, 22-Jun-2019.) The precise definition is irrelevant and should generally not be used. (New usage is discouraged.)

Assertion

Ref	Expression
df-bj-inftyexpi	⊢ inftyexpi = (𝑥 ∈ (-π(,]π) ↦ ⟨𝑥, ℂ⟩)

Detailed syntax breakdown of Definition df-bj-inftyexpi

Step	Hyp	Ref	Expression
1		cinftyexpi 32270	. 2 class inftyexpi
2		vx	. . 3 setvar 𝑥
3		cpi 14636	. . . . 5 class π
4	3	cneg 10146	. . . 4 class -π
5		cioc 12047	. . . 4 class (,]
6	4, 3, 5	co 6549	. . 3 class (-π(,]π)
7	2	cv 1474	. . . 4 class 𝑥
8		cc 9813	. . . 4 class ℂ
9	7, 8	cop 4131	. . 3 class ⟨𝑥, ℂ⟩
10	2, 6, 9	cmpt 4643	. 2 class (𝑥 ∈ (-π(,]π) ↦ ⟨𝑥, ℂ⟩)
11	1, 10	wceq 1475	1 wff inftyexpi = (𝑥 ∈ (-π(,]π) ↦ ⟨𝑥, ℂ⟩)

This definition is referenced by:  bj-inftyexpiinv  32272  bj-inftyexpidisj  32274  bj-ccinftydisj  32277  bj-elccinfty  32278  bj-minftyccb  32289