Definition df-ioo

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

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

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cioo	⊢ (,)
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	3	cv	⊢ 𝑦
10	7 9 6	wbr	⊢ 𝑧 < 𝑦
11	8 10	wa	⊢ ( 𝑥 < 𝑧 ∧ 𝑧 < 𝑦 )
12	11 4 2	crab	⊢ { 𝑧 ∈ ℝ* ∣ ( 𝑥 < 𝑧 ∧ 𝑧 < 𝑦 ) }
13	1 3 2 2 12	cmpo	⊢ ( 𝑥 ∈ ℝ* , 𝑦 ∈ ℝ* ↦ { 𝑧 ∈ ℝ* ∣ ( 𝑥 < 𝑧 ∧ 𝑧 < 𝑦 ) } )
14	0 13	wceq	⊢ (,) = ( 𝑥 ∈ ℝ* , 𝑦 ∈ ℝ* ↦ { 𝑧 ∈ ℝ* ∣ ( 𝑥 < 𝑧 ∧ 𝑧 < 𝑦 ) } )