Definition df-ioo 9562

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

Assertion

Ref	Expression
df-ioo	|- (,) = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )

Distinct variable group:   x, y, z

Detailed syntax breakdown of Definition df-ioo

Step	Hyp	Ref	Expression
1		cioo 9558	. 2 class (,)
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cxr 7717	. . 3 class RR*
5	2	cv 1311	. . . . . 6 class x
6		vz	. . . . . . 7 setvar z
7	6	cv 1311	. . . . . 6 class z
8		clt 7718	. . . . . 6 class <
9	5, 7, 8	wbr 3893	. . . . 5 wff x < z
10	3	cv 1311	. . . . . 6 class y
11	7, 10, 8	wbr 3893	. . . . 5 wff z < y
12	9, 11	wa 103	. . . 4 wff ( x < z /\ z < y )
13	12, 6, 4	crab 2392	. . 3 class { z e. RR* | ( x < z /\ z < y ) }
14	2, 3, 4, 4, 13	cmpo 5728	. 2 class ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )
15	1, 14	wceq 1312	1 wff (,) = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )

This definition is referenced by:  iooex  9577  iooval  9578  elioo3g  9580  elioo1  9581  iooss1  9586  iooss2  9587  eliooxr  9597  iccssioo  9612  ioossicc  9629  ioossico  9632  iocssioo  9633  icossioo  9634  ioossioo  9635  ioof  9641  ioodisj  9663