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Definition df-ioc 10656
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
StepHypRef Expression
1 cioc 10652 . 2  class  (,]
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cxr 8862 . . 3  class  RR*
52cv 1623 . . . . . 6  class  x
6 vz . . . . . . 7  set  z
76cv 1623 . . . . . 6  class  z
8 clt 8863 . . . . . 6  class  <
95, 7, 8wbr 4025 . . . . 5  wff  x  < 
z
103cv 1623 . . . . . 6  class  y
11 cle 8864 . . . . . 6  class  <_
127, 10, 11wbr 4025 . . . . 5  wff  z  <_ 
y
139, 12wa 360 . . . 4  wff  ( x  <  z  /\  z  <_  y )
1413, 6, 4crab 2549 . . 3  class  { z  e.  RR*  |  (
x  <  z  /\  z  <_  y ) }
152, 3, 4, 4, 14cmpt2 5822 . 2  class  ( x  e.  RR* ,  y  e. 
RR*  |->  { z  e. 
RR*  |  ( x  <  z  /\  z  <_ 
y ) } )
161, 15wceq 1624 1  wff  (,]  =  ( x  e.  RR* ,  y  e.  RR*  |->  { z  e.  RR*  |  (
x  <  z  /\  z  <_  y ) } )
Colors of variables: wff set class
This definition is referenced by:  iocval  10688  elioc1  10693  iocssxr  10728  leordtval2  16937  iocpnfordt  16940  lecldbas  16944  pnfnei  16945  iocmnfcld  18273  xrtgioo  18307  ismbf3d  19004  dvloglem  19990  iocf  25042
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