Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  df-icc GIF version

Definition df-icc 8764
 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 8760 . 2 class [,]
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 cxr 7059 . . 3 class *
52cv 1242 . . . . . 6 class 𝑥
6 vz . . . . . . 7 setvar 𝑧
76cv 1242 . . . . . 6 class 𝑧
8 cle 7061 . . . . . 6 class
95, 7, 8wbr 3764 . . . . 5 wff 𝑥𝑧
103cv 1242 . . . . . 6 class 𝑦
117, 10, 8wbr 3764 . . . . 5 wff 𝑧𝑦
129, 11wa 97 . . . 4 wff (𝑥𝑧𝑧𝑦)
1312, 6, 4crab 2310 . . 3 class {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)}
142, 3, 4, 4, 13cmpt2 5514 . 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)})
151, 14wceq 1243 1 wff [,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥𝑧𝑧𝑦)})
 Colors of variables: wff set class This definition is referenced by:  iccval  8789  elicc1  8793  iccss  8810  iccssioo  8811  iccss2  8813  iccssico  8814  iccssxr  8825  ioossicc  8828  icossicc  8829  iocssicc  8830  iccf  8841  ioodisj  8861
 Copyright terms: Public domain W3C validator