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Definition df-fm 17633
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 17628 . 2  class  FilMap
2 vx . . 3  set  x
3 vf . . 3  set  f
4 cvv 2788 . . 3  class  _V
5 vy . . . 4  set  y
63cv 1622 . . . . . 6  class  f
76cdm 4689 . . . . 5  class  dom  f
8 cfbas 17518 . . . . 5  class  fBas
97, 8cfv 5255 . . . 4  class  ( fBas `  dom  f )
102cv 1622 . . . . 5  class  x
11 vt . . . . . . 7  set  t
125cv 1622 . . . . . . 7  class  y
1311cv 1622 . . . . . . . 8  class  t
146, 13cima 4692 . . . . . . 7  class  ( f
" t )
1511, 12, 14cmpt 4077 . . . . . 6  class  ( t  e.  y  |->  ( f
" t ) )
1615crn 4690 . . . . 5  class  ran  (
t  e.  y  |->  ( f " t ) )
17 cfg 17519 . . . . 5  class  filGen
1810, 16, 17co 5858 . . . 4  class  ( x
filGen ran  ( t  e.  y  |->  ( f "
t ) ) )
195, 9, 18cmpt 4077 . . 3  class  ( y  e.  ( fBas `  dom  f )  |->  ( x
filGen ran  ( t  e.  y  |->  ( f "
t ) ) ) )
202, 3, 4, 4, 19cmpt2 5860 . 2  class  ( x  e.  _V ,  f  e.  _V  |->  ( y  e.  ( fBas `  dom  f )  |->  ( x
filGen ran  ( t  e.  y  |->  ( f "
t ) ) ) ) )
211, 20wceq 1623 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  17638  fmf  17640
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