Definition df-ioo 9678

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 9674	. 2 class (,)
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cxr 7802	. . 3 class RR*
5	2	cv 1330	. . . . . 6 class x
6		vz	. . . . . . 7 setvar z
7	6	cv 1330	. . . . . 6 class z
8		clt 7803	. . . . . 6 class <
9	5, 7, 8	wbr 3929	. . . . 5 wff x < z
10	3	cv 1330	. . . . . 6 class y
11	7, 10, 8	wbr 3929	. . . . 5 wff z < y
12	9, 11	wa 103	. . . 4 wff ( x < z /\ z < y )
13	12, 6, 4	crab 2420	. . 3 class { z e. RR* | ( x < z /\ z < y ) }
14	2, 3, 4, 4, 13	cmpo 5776	. 2 class ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )
15	1, 14	wceq 1331	1 wff (,) = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )

This definition is referenced by:  iooex  9693  iooval  9694  elioo3g  9696  elioo1  9697  iooss1  9702  iooss2  9703  eliooxr  9713  iccssioo  9728  ioossicc  9745  ioossico  9748  iocssioo  9749  icossioo  9750  ioossioo  9751  ioof  9757  ioodisj  9779