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Definition df-hodif 22328
Description: Define the difference of two Hilbert space operators. Definition of [Beran] p. 111. (Contributed by NM, 9-Nov-2000.) (New usage is discouraged.)
Assertion
Ref Expression
df-hodif  |-  -op  =  ( f  e.  ( ~H  ^m  ~H ) ,  g  e.  ( ~H  ^m  ~H )  |->  ( x  e.  ~H  |->  ( ( f `  x
)  -h  ( g `
 x ) ) ) )
Distinct variable group:    f, g, x

Detailed syntax breakdown of Definition df-hodif
StepHypRef Expression
1 chod 21536 . 2  class  -op
2 vf . . 3  set  f
3 vg . . 3  set  g
4 chil 21515 . . . 4  class  ~H
5 cmap 6788 . . . 4  class  ^m
64, 4, 5co 5874 . . 3  class  ( ~H 
^m  ~H )
7 vx . . . 4  set  x
87cv 1631 . . . . . 6  class  x
92cv 1631 . . . . . 6  class  f
108, 9cfv 5271 . . . . 5  class  ( f `
 x )
113cv 1631 . . . . . 6  class  g
128, 11cfv 5271 . . . . 5  class  ( g `
 x )
13 cmv 21521 . . . . 5  class  -h
1410, 12, 13co 5874 . . . 4  class  ( ( f `  x )  -h  ( g `  x ) )
157, 4, 14cmpt 4093 . . 3  class  ( x  e.  ~H  |->  ( ( f `  x )  -h  ( g `  x ) ) )
162, 3, 6, 6, 15cmpt2 5876 . 2  class  ( f  e.  ( ~H  ^m  ~H ) ,  g  e.  ( ~H  ^m  ~H )  |->  ( x  e. 
~H  |->  ( ( f `
 x )  -h  ( g `  x
) ) ) )
171, 16wceq 1632 1  wff  -op  =  ( f  e.  ( ~H  ^m  ~H ) ,  g  e.  ( ~H  ^m  ~H )  |->  ( x  e.  ~H  |->  ( ( f `  x
)  -h  ( g `
 x ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  hodmval  22333
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