Definition df-ioc 9985

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

Assertion

Ref	Expression
df-ioc	|- (,] = ( 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-ioc

Step	Hyp	Ref	Expression
1		cioc 9981	. 2 class (,]
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cxr 8077	. . 3 class RR*
5	2	cv 1363	. . . . . 6 class x
6		vz	. . . . . . 7 setvar z
7	6	cv 1363	. . . . . 6 class z
8		clt 8078	. . . . . 6 class <
9	5, 7, 8	wbr 4034	. . . . 5 wff x < z
10	3	cv 1363	. . . . . 6 class y
11		cle 8079	. . . . . 6 class <_
12	7, 10, 11	wbr 4034	. . . . 5 wff z <_ y
13	9, 12	wa 104	. . . 4 wff ( x < z /\ z <_ y )
14	13, 6, 4	crab 2479	. . 3 class { z e. RR* | ( x < z /\ z <_ y ) }
15	2, 3, 4, 4, 14	cmpo 5927	. 2 class ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z <_ y ) } )
16	1, 15	wceq 1364	1 wff (,] = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z <_ y ) } )

This definition is referenced by:  iocval  10010  elioc1  10014  iocssxr  10049  iocssicc  10053  iocssioo  10055