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Definition df-fm 17958
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 17953 . 2  class  FilMap
2 vx . . 3  set  x
3 vf . . 3  set  f
4 cvv 2948 . . 3  class  _V
5 vy . . . 4  set  y
63cv 1651 . . . . . 6  class  f
76cdm 4869 . . . . 5  class  dom  f
8 cfbas 16677 . . . . 5  class  fBas
97, 8cfv 5445 . . . 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 4872 . . . . . . 7  class  ( f
" t )
1511, 12, 14cmpt 4258 . . . . . 6  class  ( t  e.  y  |->  ( f
" t ) )
1615crn 4870 . . . . 5  class  ran  (
t  e.  y  |->  ( f " t ) )
17 cfg 16678 . . . . 5  class  filGen
1810, 16, 17co 6072 . . . 4  class  ( x
filGen ran  ( t  e.  y  |->  ( f "
t ) ) )
195, 9, 18cmpt 4258 . . 3  class  ( y  e.  ( fBas `  dom  f )  |->  ( x
filGen ran  ( t  e.  y  |->  ( f "
t ) ) ) )
202, 3, 4, 4, 19cmpt2 6074 . 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  17963  fmf  17965
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