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Definition df-fm 17970
Description: Define a function that takes a filter to a neighborhood filter of the range. (Since we now allow filter bases to have support smaller than the base set, the function has to come first to ensure that curryings are sets.) (Contributed by Jeff Hankins, 5-Sep-2009.) (Revised by Stefan O'Rear, 20-Jul-2015.)
Assertion
Ref Expression
df-fm  |-  FilMap  =  ( x  e.  _V , 
f  e.  _V  |->  ( y  e.  ( fBas `  dom  f )  |->  ( x filGen ran  ( t  e.  y  |->  ( f
" t ) ) ) ) )
Distinct variable group:    t, f, x, y

Detailed syntax breakdown of Definition df-fm
StepHypRef Expression
1 cfm 17965 . 2  class  FilMap
2 vx . . 3  set  x
3 vf . . 3  set  f
4 cvv 2956 . . 3  class  _V
5 vy . . . 4  set  y
63cv 1651 . . . . . 6  class  f
76cdm 4878 . . . . 5  class  dom  f
8 cfbas 16689 . . . . 5  class  fBas
97, 8cfv 5454 . . . 4  class  ( fBas `  dom  f )
102cv 1651 . . . . 5  class  x
11 vt . . . . . . 7  set  t
125cv 1651 . . . . . . 7  class  y
1311cv 1651 . . . . . . . 8  class  t
146, 13cima 4881 . . . . . . 7  class  ( f
" t )
1511, 12, 14cmpt 4266 . . . . . 6  class  ( t  e.  y  |->  ( f
" t ) )
1615crn 4879 . . . . 5  class  ran  (
t  e.  y  |->  ( f " t ) )
17 cfg 16690 . . . . 5  class  filGen
1810, 16, 17co 6081 . . . 4  class  ( x
filGen ran  ( t  e.  y  |->  ( f "
t ) ) )
195, 9, 18cmpt 4266 . . 3  class  ( y  e.  ( fBas `  dom  f )  |->  ( x
filGen ran  ( t  e.  y  |->  ( f "
t ) ) ) )
202, 3, 4, 4, 19cmpt2 6083 . 2  class  ( x  e.  _V ,  f  e.  _V  |->  ( y  e.  ( fBas `  dom  f )  |->  ( x
filGen ran  ( t  e.  y  |->  ( f "
t ) ) ) ) )
211, 20wceq 1652 1  wff  FilMap  =  ( x  e.  _V , 
f  e.  _V  |->  ( y  e.  ( fBas `  dom  f )  |->  ( x filGen ran  ( t  e.  y  |->  ( f
" t ) ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  fmval  17975  fmf  17977
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