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Definition df-fi 7378
Description: Function whose value is the class of all the finite intersections of the elements of  x. (Contributed by FL, 27-Apr-2008.)
Assertion
Ref Expression
df-fi  |-  fi  =  ( x  e.  _V  |->  { z  |  E. y  e.  ( ~P x  i^i  Fin ) z  =  |^| y } )
Distinct variable group:    x, y, z

Detailed syntax breakdown of Definition df-fi
StepHypRef Expression
1 cfi 7377 . 2  class  fi
2 vx . . 3  set  x
3 cvv 2920 . . 3  class  _V
4 vz . . . . . . 7  set  z
54cv 1648 . . . . . 6  class  z
6 vy . . . . . . . 8  set  y
76cv 1648 . . . . . . 7  class  y
87cint 4014 . . . . . 6  class  |^| y
95, 8wceq 1649 . . . . 5  wff  z  = 
|^| y
102cv 1648 . . . . . . 7  class  x
1110cpw 3763 . . . . . 6  class  ~P x
12 cfn 7072 . . . . . 6  class  Fin
1311, 12cin 3283 . . . . 5  class  ( ~P x  i^i  Fin )
149, 6, 13wrex 2671 . . . 4  wff  E. y  e.  ( ~P x  i^i 
Fin ) z  = 
|^| y
1514, 4cab 2394 . . 3  class  { z  |  E. y  e.  ( ~P x  i^i 
Fin ) z  = 
|^| y }
162, 3, 15cmpt 4230 . 2  class  ( x  e.  _V  |->  { z  |  E. y  e.  ( ~P x  i^i 
Fin ) z  = 
|^| y } )
171, 16wceq 1649 1  wff  fi  =  ( x  e.  _V  |->  { z  |  E. y  e.  ( ~P x  i^i  Fin ) z  =  |^| y } )
Colors of variables: wff set class
This definition is referenced by:  fival  7379
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