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Definition df-ioc 12218
Description: Define the set of open-below, closed-above intervals of extended reals. (Contributed by NM, 24-Dec-2006.)
Assertion
Ref Expression
df-ioc (,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)})
Distinct variable group:   𝑥,𝑦,𝑧

Detailed syntax breakdown of Definition df-ioc
StepHypRef Expression
1 cioc 12214 . 2 class (,]
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cxr 10111 . . 3 class *
52cv 1522 . . . . . 6 class 𝑥
6 vz . . . . . . 7 setvar 𝑧
76cv 1522 . . . . . 6 class 𝑧
8 clt 10112 . . . . . 6 class <
95, 7, 8wbr 4685 . . . . 5 wff 𝑥 < 𝑧
103cv 1522 . . . . . 6 class 𝑦
11 cle 10113 . . . . . 6 class
127, 10, 11wbr 4685 . . . . 5 wff 𝑧𝑦
139, 12wa 383 . . . 4 wff (𝑥 < 𝑧𝑧𝑦)
1413, 6, 4crab 2945 . . 3 class {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)}
152, 3, 4, 4, 14cmpt2 6692 . 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)})
161, 15wceq 1523 1 wff (,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)})
Colors of variables: wff setvar class
This definition is referenced by:  iocval  12250  elioc1  12255  iocssxr  12295  iocssicc  12299  iocssioo  12301  snunioc  12338  leordtval2  21064  iocpnfordt  21067  lecldbas  21071  pnfnei  21072  iocmnfcld  22619  xrtgioo  22656  ismbf3d  23466  dvloglem  24439  asindmre  33625  dvasin  33626  ioounsn  38112  ioossioc  40031  snunioo2  40049  eliocre  40052  lbioc  40057
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