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Definition df-icc 13394
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 13390 . 2 class [,]
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cxr 11294 . . 3 class *
52cv 1539 . . . . . 6 class 𝑥
6 vz . . . . . . 7 setvar 𝑧
76cv 1539 . . . . . 6 class 𝑧
8 cle 11296 . . . . . 6 class
95, 7, 8wbr 5143 . . . . 5 wff 𝑥𝑧
103cv 1539 . . . . . 6 class 𝑦
117, 10, 8wbr 5143 . . . . 5 wff 𝑧𝑦
129, 11wa 395 . . . 4 wff (𝑥𝑧𝑧𝑦)
1312, 6, 4crab 3436 . . 3 class {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)}
142, 3, 4, 4, 13cmpo 7433 . 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)})
151, 14wceq 1540 1 wff [,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)})
Colors of variables: wff setvar class
This definition is referenced by:  iccval  13426  elicc1  13431  iccss  13455  iccssioo  13456  iccss2  13458  iccssico  13459  iccssxr  13470  ioossicc  13473  icossicc  13476  iocssicc  13477  iccf  13488  ioounsn  13517  snunioo  13518  snunico  13519  snunioc  13520  ioodisj  13522  leordtval2  23220  iccordt  23222  lecldbas  23227  ioombl  25600  itgspliticc  25872  psercnlem2  26468  tanord1  26579  cvmliftlem10  35299  ftc1anclem7  37706  ftc1anclem8  37707  ftc1anc  37708  snunioo1  45525  iccin  48794  iccdisj2  48795
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