Definition df-icc 9708

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* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)})

Distinct variable group:   𝑥,𝑦,𝑧

Detailed syntax breakdown of Definition df-icc

Step	Hyp	Ref	Expression
1		cicc 9704	. 2 class [,]
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cxr 7823	. . 3 class ℝ*
5	2	cv 1331	. . . . . 6 class 𝑥
6		vz	. . . . . . 7 setvar 𝑧
7	6	cv 1331	. . . . . 6 class 𝑧
8		cle 7825	. . . . . 6 class ≤
9	5, 7, 8	wbr 3937	. . . . 5 wff 𝑥 ≤ 𝑧
10	3	cv 1331	. . . . . 6 class 𝑦
11	7, 10, 8	wbr 3937	. . . . 5 wff 𝑧 ≤ 𝑦
12	9, 11	wa 103	. . . 4 wff (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)
13	12, 6, 4	crab 2421	. . 3 class {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)}
14	2, 3, 4, 4, 13	cmpo 5784	. 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)})
15	1, 14	wceq 1332	1 wff [,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)})

This definition is referenced by:  iccval  9733  elicc1  9737  iccss  9754  iccssioo  9755  iccss2  9757  iccssico  9758  iccssxr  9769  ioossicc  9772  icossicc  9773  iocssicc  9774  iccf  9785  ioodisj  9806