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Definition df-icc 8865
Description: Define the set of closed intervals of extended reals. (Contributed by NM, 24-Dec-2006.)
Assertion
Ref Expression
df-icc [,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)})
Distinct variable group:   𝑥,𝑦,𝑧

Detailed syntax breakdown of Definition df-icc
StepHypRef Expression
1 cicc 8861 . 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 cle 7120 . . . . . 6 class
95, 7, 8wbr 3792 . . . . 5 wff 𝑥𝑧
103cv 1258 . . . . . 6 class 𝑦
117, 10, 8wbr 3792 . . . . 5 wff 𝑧𝑦
129, 11wa 101 . . . 4 wff (𝑥𝑧𝑧𝑦)
1312, 6, 4crab 2327 . . 3 class {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)}
142, 3, 4, 4, 13cmpt2 5542 . 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)})
151, 14wceq 1259 1 wff [,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)})
Colors of variables: wff set class
This definition is referenced by:  iccval  8890  elicc1  8894  iccss  8911  iccssioo  8912  iccss2  8914  iccssico  8915  iccssxr  8926  ioossicc  8929  icossicc  8930  iocssicc  8931  iccf  8942  ioodisj  8962
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