Definition df-ico 9460

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 9456	. 2 class [,)
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cxr 7618	. . 3 class RR*
5	2	cv 1295	. . . . . 6 class x
6		vz	. . . . . . 7 setvar z
7	6	cv 1295	. . . . . 6 class z
8		cle 7620	. . . . . 6 class <_
9	5, 7, 8	wbr 3867	. . . . 5 wff x <_ z
10	3	cv 1295	. . . . . 6 class y
11		clt 7619	. . . . . 6 class <
12	7, 10, 11	wbr 3867	. . . . 5 wff z < y
13	9, 12	wa 103	. . . 4 wff ( x <_ z /\ z < y )
14	13, 6, 4	crab 2374	. . 3 class { z e. RR* | ( x <_ z /\ z < y ) }
15	2, 3, 4, 4, 14	cmpt2 5692	. 2 class ( x e. RR* , y e. RR* |-> { z e. RR* | ( x <_ z /\ z < y ) } )
16	1, 15	wceq 1296	1 wff [,) = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x <_ z /\ z < y ) } )

This definition is referenced by:  icoval  9485  elico1  9489  icossico  9509  iccssico  9511  iccssico2  9513  icossxr  9524  icossicc  9526  ioossico  9528  icossioo  9530