Definition df-ioc 10877

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 10873	. 2 class (,]
2		vx	. . 3 set x
3		vy	. . 3 set y
4		cxr 9075	. . 3 class RR*
5	2	cv 1648	. . . . . 6 class x
6		vz	. . . . . . 7 set z
7	6	cv 1648	. . . . . 6 class z
8		clt 9076	. . . . . 6 class <
9	5, 7, 8	wbr 4172	. . . . 5 wff x < z
10	3	cv 1648	. . . . . 6 class y
11		cle 9077	. . . . . 6 class <_
12	7, 10, 11	wbr 4172	. . . . 5 wff z <_ y
13	9, 12	wa 359	. . . 4 wff ( x < z /\ z <_ y )
14	13, 6, 4	crab 2670	. . 3 class { z e. RR* | ( x < z /\ z <_ y ) }
15	2, 3, 4, 4, 14	cmpt2 6042	. 2 class ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z <_ y ) } )
16	1, 15	wceq 1649	1 wff (,] = ( x e. RR* , y e. RR* |-> { z e. RR* | ( x < z /\ z <_ y ) } )

This definition is referenced by:  iocval  10909  elioc1  10914  iocssxr  10950  leordtval2  17230  iocpnfordt  17233  lecldbas  17237  pnfnei  17238  iocmnfcld  18756  xrtgioo  18790  ismbf3d  19499  dvloglem  20492  iocssicc  24083  iocssioo  24085  snunioc  24090