Definition df-ioc

Description: Define the set of open-below, closed-above intervals of extended reals. (Contributed by NM, 24-Dec-2006)

	Ref	Expression
Assertion	df-ioc	⊢ (,] = ( 𝑥 ∈ ℝ* , 𝑦 ∈ ℝ* ↦ { 𝑧 ∈ ℝ* ∣ ( 𝑥 < 𝑧 ∧ 𝑧 ≤ 𝑦 ) } )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cioc	⊢ (,]
1		vx	⊢ 𝑥
2		cxr	⊢ ℝ*
3		vy	⊢ 𝑦
4		vz	⊢ 𝑧
5	1	cv	⊢ 𝑥
6		clt	⊢ <
7	4	cv	⊢ 𝑧
8	5 7 6	wbr	⊢ 𝑥 < 𝑧
9		cle	⊢ ≤
10	3	cv	⊢ 𝑦
11	7 10 9	wbr	⊢ 𝑧 ≤ 𝑦
12	8 11	wa	⊢ ( 𝑥 < 𝑧 ∧ 𝑧 ≤ 𝑦 )
13	12 4 2	crab	⊢ { 𝑧 ∈ ℝ* ∣ ( 𝑥 < 𝑧 ∧ 𝑧 ≤ 𝑦 ) }
14	1 3 2 2 13	cmpo	⊢ ( 𝑥 ∈ ℝ* , 𝑦 ∈ ℝ* ↦ { 𝑧 ∈ ℝ* ∣ ( 𝑥 < 𝑧 ∧ 𝑧 ≤ 𝑦 ) } )
15	0 14	wceq	⊢ (,] = ( 𝑥 ∈ ℝ* , 𝑦 ∈ ℝ* ↦ { 𝑧 ∈ ℝ* ∣ ( 𝑥 < 𝑧 ∧ 𝑧 ≤ 𝑦 ) } )