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Definition df-icc 8994
Description: Define the set of closed intervals of extended reals. (Contributed by NM, 24-Dec-2006.)
Assertion
Ref Expression
df-icc  |-  [,]  =  ( 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-icc
StepHypRef Expression
1 cicc 8990 . 2  class  [,]
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 cxr 7214 . . 3  class  RR*
52cv 1284 . . . . . 6  class  x
6 vz . . . . . . 7  setvar  z
76cv 1284 . . . . . 6  class  z
8 cle 7216 . . . . . 6  class  <_
95, 7, 8wbr 3793 . . . . 5  wff  x  <_ 
z
103cv 1284 . . . . . 6  class  y
117, 10, 8wbr 3793 . . . . 5  wff  z  <_ 
y
129, 11wa 102 . . . 4  wff  ( x  <_  z  /\  z  <_  y )
1312, 6, 4crab 2353 . . 3  class  { z  e.  RR*  |  (
x  <_  z  /\  z  <_  y ) }
142, 3, 4, 4, 13cmpt2 5545 . 2  class  ( x  e.  RR* ,  y  e. 
RR*  |->  { z  e. 
RR*  |  ( x  <_  z  /\  z  <_ 
y ) } )
151, 14wceq 1285 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:  iccval  9019  elicc1  9023  iccss  9040  iccssioo  9041  iccss2  9043  iccssico  9044  iccssxr  9055  ioossicc  9058  icossicc  9059  iocssicc  9060  iccf  9071  ioodisj  9091
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