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Definition df-ioc 13383
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 13379 . 2 class (,]
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cxr 11297 . . 3 class *
52cv 1533 . . . . . 6 class 𝑥
6 vz . . . . . . 7 setvar 𝑧
76cv 1533 . . . . . 6 class 𝑧
8 clt 11298 . . . . . 6 class <
95, 7, 8wbr 5153 . . . . 5 wff 𝑥 < 𝑧
103cv 1533 . . . . . 6 class 𝑦
11 cle 11299 . . . . . 6 class
127, 10, 11wbr 5153 . . . . 5 wff 𝑧𝑦
139, 12wa 394 . . . 4 wff (𝑥 < 𝑧𝑧𝑦)
1413, 6, 4crab 3419 . . 3 class {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)}
152, 3, 4, 4, 14cmpo 7426 . 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)})
161, 15wceq 1534 1 wff (,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)})
Colors of variables: wff setvar class
This definition is referenced by:  iocval  13415  elioc1  13420  iocssxr  13462  iocssicc  13468  iocssioo  13470  ioounsn  13508  snunioc  13511  leordtval2  23207  iocpnfordt  23210  lecldbas  23214  pnfnei  23215  iocmnfcld  24776  xrtgioo  24813  ismbf3d  25674  dvloglem  26675  asindmre  37404  dvasin  37405  ioossioc  45110  eliocre  45127  lbioc  45131
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