Definition df-ioo 9967

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 9963	. 2 class (,)
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cxr 8060	. . 3 class RR*
5	2	cv 1363	. . . . . 6 class x
6		vz	. . . . . . 7 setvar z
7	6	cv 1363	. . . . . 6 class z
8		clt 8061	. . . . . 6 class <
9	5, 7, 8	wbr 4033	. . . . 5 wff x < z
10	3	cv 1363	. . . . . 6 class y
11	7, 10, 8	wbr 4033	. . . . 5 wff z < y
12	9, 11	wa 104	. . . 4 wff ( x < z /\ z < y )
13	12, 6, 4	crab 2479	. . 3 class { z e. RR* | ( x < z /\ z < y ) }
14	2, 3, 4, 4, 13	cmpo 5924	. 2 class ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )
15	1, 14	wceq 1364	1 wff (,) = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )

This definition is referenced by:  iooex  9982  iooval  9983  elioo3g  9985  elioo1  9986  iooss1  9991  iooss2  9992  eliooxr  10002  iccssioo  10017  ioossicc  10034  ioossico  10037  iocssioo  10038  icossioo  10039  ioossioo  10040  ioof  10046  ioodisj  10068