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Definition df-fm 17729
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 17724 . 2  class  FilMap
2 vx . . 3  set  x
3 vf . . 3  set  f
4 cvv 2864 . . 3  class  _V
5 vy . . . 4  set  y
63cv 1641 . . . . . 6  class  f
76cdm 4768 . . . . 5  class  dom  f
8 cfbas 16465 . . . . 5  class  fBas
97, 8cfv 5334 . . . 4  class  ( fBas `  dom  f )
102cv 1641 . . . . 5  class  x
11 vt . . . . . . 7  set  t
125cv 1641 . . . . . . 7  class  y
1311cv 1641 . . . . . . . 8  class  t
146, 13cima 4771 . . . . . . 7  class  ( f
" t )
1511, 12, 14cmpt 4156 . . . . . 6  class  ( t  e.  y  |->  ( f
" t ) )
1615crn 4769 . . . . 5  class  ran  (
t  e.  y  |->  ( f " t ) )
17 cfg 16466 . . . . 5  class  filGen
1810, 16, 17co 5942 . . . 4  class  ( x
filGen ran  ( t  e.  y  |->  ( f "
t ) ) )
195, 9, 18cmpt 4156 . . 3  class  ( y  e.  ( fBas `  dom  f )  |->  ( x
filGen ran  ( t  e.  y  |->  ( f "
t ) ) ) )
202, 3, 4, 4, 19cmpt2 5944 . 2  class  ( x  e.  _V ,  f  e.  _V  |->  ( y  e.  ( fBas `  dom  f )  |->  ( x
filGen ran  ( t  e.  y  |->  ( f "
t ) ) ) ) )
211, 20wceq 1642 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  17734  fmf  17736
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