Definition df-ico 10090

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

Assertion

Ref	Expression
df-ico	|- [,) = ( 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-ico

Step	Hyp	Ref	Expression
1		cico 10086	. 2 class [,)
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cxr 8180	. . 3 class RR*
5	2	cv 1394	. . . . . 6 class x
6		vz	. . . . . . 7 setvar z
7	6	cv 1394	. . . . . 6 class z
8		cle 8182	. . . . . 6 class <_
9	5, 7, 8	wbr 4083	. . . . 5 wff x <_ z
10	3	cv 1394	. . . . . 6 class y
11		clt 8181	. . . . . 6 class <
12	7, 10, 11	wbr 4083	. . . . 5 wff z < y
13	9, 12	wa 104	. . . 4 wff ( x <_ z /\ z < y )
14	13, 6, 4	crab 2512	. . 3 class { z e. RR* | ( x <_ z /\ z < y ) }
15	2, 3, 4, 4, 14	cmpo 6003	. 2 class ( x e. RR* , y e. RR* |-> { z e. RR* | ( x <_ z /\ z < y ) } )
16	1, 15	wceq 1395	1 wff [,) = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x <_ z /\ z < y ) } )

This definition is referenced by:  icoval  10115  elico1  10119  icossico  10139  iccssico  10141  iccssico2  10143  icossxr  10154  icossicc  10156  ioossico  10158  icossioo  10160  elicore  10486