MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-fz Unicode version

Definition df-fz 11028
Description: Define an operation that produces a finite set of sequential integers. Read " M ... N " as "the set of integers from  M to  N inclusive." See fzval 11029 for its value and additional comments. (Contributed by NM, 6-Sep-2005.)
Assertion
Ref Expression
df-fz  |-  ...  =  ( m  e.  ZZ ,  n  e.  ZZ  |->  { k  e.  ZZ  |  ( m  <_ 
k  /\  k  <_  n ) } )
Distinct variable group:    m, n, k

Detailed syntax breakdown of Definition df-fz
StepHypRef Expression
1 cfz 11027 . 2  class  ...
2 vm . . 3  set  m
3 vn . . 3  set  n
4 cz 10266 . . 3  class  ZZ
52cv 1651 . . . . . 6  class  m
6 vk . . . . . . 7  set  k
76cv 1651 . . . . . 6  class  k
8 cle 9105 . . . . . 6  class  <_
95, 7, 8wbr 4199 . . . . 5  wff  m  <_ 
k
103cv 1651 . . . . . 6  class  n
117, 10, 8wbr 4199 . . . . 5  wff  k  <_  n
129, 11wa 359 . . . 4  wff  ( m  <_  k  /\  k  <_  n )
1312, 6, 4crab 2696 . . 3  class  { k  e.  ZZ  |  ( m  <_  k  /\  k  <_  n ) }
142, 3, 4, 4, 13cmpt2 6069 . 2  class  ( m  e.  ZZ ,  n  e.  ZZ  |->  { k  e.  ZZ  |  ( m  <_  k  /\  k  <_  n ) } )
151, 14wceq 1652 1  wff  ...  =  ( m  e.  ZZ ,  n  e.  ZZ  |->  { k  e.  ZZ  |  ( m  <_ 
k  /\  k  <_  n ) } )
Colors of variables: wff set class
This definition is referenced by:  fzval  11029  fzf  11031
  Copyright terms: Public domain W3C validator