Definition df-icc 13282

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 13278	. 2 class [,]
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cxr 11179	. . 3 class ℝ*
5	2	cv 1541	. . . . . 6 class 𝑥
6		vz	. . . . . . 7 setvar 𝑧
7	6	cv 1541	. . . . . 6 class 𝑧
8		cle 11181	. . . . . 6 class ≤
9	5, 7, 8	wbr 5100	. . . . 5 wff 𝑥 ≤ 𝑧
10	3	cv 1541	. . . . . 6 class 𝑦
11	7, 10, 8	wbr 5100	. . . . 5 wff 𝑧 ≤ 𝑦
12	9, 11	wa 395	. . . 4 wff (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)
13	12, 6, 4	crab 3401	. . 3 class {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)}
14	2, 3, 4, 4, 13	cmpo 7372	. 2 class (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)})
15	1, 14	wceq 1542	1 wff [,] = (𝑥 ∈ ℝ*, 𝑦 ∈ ℝ* ↦ {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)})

This definition is referenced by:  iccval  13314  elicc1  13319  iccss  13344  iccssioo  13345  iccss2  13347  iccssico  13348  iccssxr  13360  ioossicc  13363  icossicc  13366  iocssicc  13367  iccf  13378  ioounsn  13407  snunioo  13408  snunico  13409  snunioc  13410  ioodisj  13412  leordtval2  23173  iccordt  23175  lecldbas  23180  ioombl  25539  itgspliticc  25811  psercnlem2  26407  tanord1  26519  cvmliftlem10  35516  ftc1anclem7  37979  ftc1anclem8  37980  ftc1anc  37981  snunioo1  45901  iccin  49284  iccdisj2  49285