Definition df-ioo 9892

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 9888	. 2 class (,)
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cxr 7991	. . 3 class RR*
5	2	cv 1352	. . . . . 6 class x
6		vz	. . . . . . 7 setvar z
7	6	cv 1352	. . . . . 6 class z
8		clt 7992	. . . . . 6 class <
9	5, 7, 8	wbr 4004	. . . . 5 wff x < z
10	3	cv 1352	. . . . . 6 class y
11	7, 10, 8	wbr 4004	. . . . 5 wff z < y
12	9, 11	wa 104	. . . 4 wff ( x < z /\ z < y )
13	12, 6, 4	crab 2459	. . 3 class { z e. RR* | ( x < z /\ z < y ) }
14	2, 3, 4, 4, 13	cmpo 5877	. 2 class ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )
15	1, 14	wceq 1353	1 wff (,) = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z < y ) } )

This definition is referenced by:  iooex  9907  iooval  9908  elioo3g  9910  elioo1  9911  iooss1  9916  iooss2  9917  eliooxr  9927  iccssioo  9942  ioossicc  9959  ioossico  9962  iocssioo  9963  icossioo  9964  ioossioo  9965  ioof  9971  ioodisj  9993