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Definition df-ioc 8863
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 8859 . 2 class (,]
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cxr 7118 . . 3 class *
52cv 1258 . . . . . 6 class 𝑥
6 vz . . . . . . 7 setvar 𝑧
76cv 1258 . . . . . 6 class 𝑧
8 clt 7119 . . . . . 6 class <
95, 7, 8wbr 3792 . . . . 5 wff 𝑥 < 𝑧
103cv 1258 . . . . . 6 class 𝑦
11 cle 7120 . . . . . 6 class
127, 10, 11wbr 3792 . . . . 5 wff 𝑧𝑦
139, 12wa 101 . . . 4 wff (𝑥 < 𝑧𝑧𝑦)
1413, 6, 4crab 2327 . . 3 class {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)}
152, 3, 4, 4, 14cmpt2 5542 . 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)})
161, 15wceq 1259 1 wff (,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 < 𝑧𝑧𝑦)})
Colors of variables: wff set class
This definition is referenced by:  iocval  8888  elioc1  8892  iocssxr  8927  iocssicc  8931  iocssioo  8933
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