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Definition df-staf 15610
Description: Define the functionalization of the involution in a star ring. This is not strictly necessary but by having  * r as an actual function we can state the principal properties of an involution much more cleanly. (Contributed by Mario Carneiro, 6-Oct-2015.)
Assertion
Ref Expression
df-staf  |-  * r f  =  ( f  e.  _V  |->  ( x  e.  ( Base `  f
)  |->  ( ( * r `  f ) `
 x ) ) )
Distinct variable group:    x, f

Detailed syntax breakdown of Definition df-staf
StepHypRef Expression
1 cstf 15608 . 2  class  * r f
2 vf . . 3  set  f
3 cvv 2788 . . 3  class  _V
4 vx . . . 4  set  x
52cv 1622 . . . . 5  class  f
6 cbs 13148 . . . . 5  class  Base
75, 6cfv 5255 . . . 4  class  ( Base `  f )
84cv 1622 . . . . 5  class  x
9 cstv 13210 . . . . . 6  class  * r
105, 9cfv 5255 . . . . 5  class  ( * r `  f )
118, 10cfv 5255 . . . 4  class  ( ( * r `  f
) `  x )
124, 7, 11cmpt 4077 . . 3  class  ( x  e.  ( Base `  f
)  |->  ( ( * r `  f ) `
 x ) )
132, 3, 12cmpt 4077 . 2  class  ( f  e.  _V  |->  ( x  e.  ( Base `  f
)  |->  ( ( * r `  f ) `
 x ) ) )
141, 13wceq 1623 1  wff  * r f  =  ( f  e.  _V  |->  ( x  e.  ( Base `  f
)  |->  ( ( * r `  f ) `
 x ) ) )
Colors of variables: wff set class
This definition is referenced by:  staffval  15612
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