Definition df-ico 10051

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 10047	. 2 class [,)
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cxr 8141	. . 3 class RR*
5	2	cv 1372	. . . . . 6 class x
6		vz	. . . . . . 7 setvar z
7	6	cv 1372	. . . . . 6 class z
8		cle 8143	. . . . . 6 class <_
9	5, 7, 8	wbr 4059	. . . . 5 wff x <_ z
10	3	cv 1372	. . . . . 6 class y
11		clt 8142	. . . . . 6 class <
12	7, 10, 11	wbr 4059	. . . . 5 wff z < y
13	9, 12	wa 104	. . . 4 wff ( x <_ z /\ z < y )
14	13, 6, 4	crab 2490	. . 3 class { z e. RR* | ( x <_ z /\ z < y ) }
15	2, 3, 4, 4, 14	cmpo 5969	. 2 class ( x e. RR* , y e. RR* |-> { z e. RR* | ( x <_ z /\ z < y ) } )
16	1, 15	wceq 1373	1 wff [,) = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x <_ z /\ z < y ) } )

This definition is referenced by:  icoval  10076  elico1  10080  icossico  10100  iccssico  10102  iccssico2  10104  icossxr  10115  icossicc  10117  ioossico  10119  icossioo  10121  elicore  10446