Definition df-ico 8917

Description: Define the set of closed-below, open-above intervals of extended reals. (Contributed by NM, 24-Dec-2006.)

Assertion

Ref	Expression
df-ico	⊢ [,) = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 < 𝑦)})

Distinct variable group:   𝑥,𝑦,𝑧

Detailed syntax breakdown of Definition df-ico

Step	Hyp	Ref	Expression
1		cico 8913	. 2 class [,)
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cxr 7152	. . 3 class ℝ*
5	2	cv 1283	. . . . . 6 class 𝑥
6		vz	. . . . . . 7 setvar 𝑧
7	6	cv 1283	. . . . . 6 class 𝑧
8		cle 7154	. . . . . 6 class ≤
9	5, 7, 8	wbr 3785	. . . . 5 wff 𝑥 ≤ 𝑧
10	3	cv 1283	. . . . . 6 class 𝑦
11		clt 7153	. . . . . 6 class <
12	7, 10, 11	wbr 3785	. . . . 5 wff 𝑧 < 𝑦
13	9, 12	wa 102	. . . 4 wff (𝑥 ≤ 𝑧 ∧ 𝑧 < 𝑦)
14	13, 6, 4	crab 2352	. . 3 class {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 < 𝑦)}
15	2, 3, 4, 4, 14	cmpt2 5534	. 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 < 𝑦)})
16	1, 15	wceq 1284	1 wff [,) = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 < 𝑦)})

This definition is referenced by:  icoval  8942  elico1  8946  icossico  8966  iccssico  8968  iccssico2  8970  icossxr  8981  icossicc  8983  ioossico  8985  icossioo  8987