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Definition df-ioc 13326
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 13322 . 2 class (,]
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cxr 11244 . . 3 class *
52cv 1541 . . . . . 6 class 𝑥
6 vz . . . . . . 7 setvar 𝑧
76cv 1541 . . . . . 6 class 𝑧
8 clt 11245 . . . . . 6 class <
95, 7, 8wbr 5148 . . . . 5 wff 𝑥 < 𝑧
103cv 1541 . . . . . 6 class 𝑦
11 cle 11246 . . . . . 6 class
127, 10, 11wbr 5148 . . . . 5 wff 𝑧𝑦
139, 12wa 397 . . . 4 wff (𝑥 < 𝑧𝑧𝑦)
1413, 6, 4crab 3433 . . 3 class {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)}
152, 3, 4, 4, 14cmpo 7408 . 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)})
161, 15wceq 1542 1 wff (,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)})
Colors of variables: wff setvar class
This definition is referenced by:  iocval  13358  elioc1  13363  iocssxr  13405  iocssicc  13411  iocssioo  13413  ioounsn  13451  snunioc  13454  leordtval2  22708  iocpnfordt  22711  lecldbas  22715  pnfnei  22716  iocmnfcld  24277  xrtgioo  24314  ismbf3d  25163  dvloglem  26148  asindmre  36560  dvasin  36561  ioossioc  44192  eliocre  44209  lbioc  44213
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