Definition df-icc 13305

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 13301	. 2 class [,]
2		vx	. . 3 setvar 𝑥
3		vy	. . 3 setvar 𝑦
4		cxr 11178	. . 3 class ℝ*
5	2	cv 1541	. . . . . 6 class 𝑥
6		vz	. . . . . . 7 setvar 𝑧
7	6	cv 1541	. . . . . 6 class 𝑧
8		cle 11180	. . . . . 6 class ≤
9	5, 7, 8	wbr 5085	. . . . 5 wff 𝑥 ≤ 𝑧
10	3	cv 1541	. . . . . 6 class 𝑦
11	7, 10, 8	wbr 5085	. . . . 5 wff 𝑧 ≤ 𝑦
12	9, 11	wa 395	. . . 4 wff (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)
13	12, 6, 4	crab 3389	. . 3 class {𝑧 ∈ ℝ* ∣ (𝑥 ≤ 𝑧 ∧ 𝑧 ≤ 𝑦)}
14	2, 3, 4, 4, 13	cmpo 7369	. 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  13337  elicc1  13342  iccss  13367  iccssioo  13368  iccss2  13370  iccssico  13371  iccssxr  13383  ioossicc  13386  icossicc  13389  iocssicc  13390  iccf  13401  ioounsn  13430  snunioo  13431  snunico  13432  snunioc  13433  ioodisj  13435  leordtval2  23177  iccordt  23179  lecldbas  23184  ioombl  25532  itgspliticc  25804  psercnlem2  26389  tanord1  26501  cvmliftlem10  35476  ftc1anclem7  38020  ftc1anclem8  38021  ftc1anc  38022  snunioo1  45942  iccin  49371  iccdisj2  49372