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 e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cioo	|- (,)
1		vx	|- x
2		cxr	|- RR*
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 e. RR* | ( x < z /\ z < y ) }
13	1 3 2 2 12	cmpo	|- ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )
14	0 13	wceq	|- (,) = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )