Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-ico GIF version

Definition df-ico 9689
 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* ∣ (𝑥𝑧𝑧 < 𝑦)})
Distinct variable group:   𝑥,𝑦,𝑧

Detailed syntax breakdown of Definition df-ico
StepHypRef Expression
1 cico 9685 . 2 class [,)
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cxr 7811 . . 3 class *
52cv 1330 . . . . . 6 class 𝑥
6 vz . . . . . . 7 setvar 𝑧
76cv 1330 . . . . . 6 class 𝑧
8 cle 7813 . . . . . 6 class
95, 7, 8wbr 3929 . . . . 5 wff 𝑥𝑧
103cv 1330 . . . . . 6 class 𝑦
11 clt 7812 . . . . . 6 class <
127, 10, 11wbr 3929 . . . . 5 wff 𝑧 < 𝑦
139, 12wa 103 . . . 4 wff (𝑥𝑧𝑧 < 𝑦)
1413, 6, 4crab 2420 . . 3 class {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧 < 𝑦)}
152, 3, 4, 4, 14cmpo 5776 . 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧 < 𝑦)})
161, 15wceq 1331 1 wff [,) = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧 < 𝑦)})
 Colors of variables: wff set class This definition is referenced by:  icoval  9714  elico1  9718  icossico  9738  iccssico  9740  iccssico2  9742  icossxr  9753  icossicc  9755  ioossico  9757  icossioo  9759
 Copyright terms: Public domain W3C validator