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Definition df-homf 14629
Description: Define the functionalized Hom-set operator, which is exactly like  Hom but is guaranteed to be a function on the base. (Contributed by Mario Carneiro, 4-Jan-2017.)
Assertion
Ref Expression
df-homf  |-  Hom f  =  (
c  e.  _V  |->  ( x  e.  ( Base `  c ) ,  y  e.  ( Base `  c
)  |->  ( x ( Hom  `  c )
y ) ) )
Distinct variable group:    x, c, y

Detailed syntax breakdown of Definition df-homf
StepHypRef Expression
1 chomf 14625 . 2  class  Hom f
2 vc . . 3  setvar  c
3 cvv 2993 . . 3  class  _V
4 vx . . . 4  setvar  x
5 vy . . . 4  setvar  y
62cv 1368 . . . . 5  class  c
7 cbs 14195 . . . . 5  class  Base
86, 7cfv 5439 . . . 4  class  ( Base `  c )
94cv 1368 . . . . 5  class  x
105cv 1368 . . . . 5  class  y
11 chom 14270 . . . . . 6  class  Hom
126, 11cfv 5439 . . . . 5  class  ( Hom  `  c )
139, 10, 12co 6112 . . . 4  class  ( x ( Hom  `  c
) y )
144, 5, 8, 8, 13cmpt2 6114 . . 3  class  ( x  e.  ( Base `  c
) ,  y  e.  ( Base `  c
)  |->  ( x ( Hom  `  c )
y ) )
152, 3, 14cmpt 4371 . 2  class  ( c  e.  _V  |->  ( x  e.  ( Base `  c
) ,  y  e.  ( Base `  c
)  |->  ( x ( Hom  `  c )
y ) ) )
161, 15wceq 1369 1  wff  Hom f  =  (
c  e.  _V  |->  ( x  e.  ( Base `  c ) ,  y  e.  ( Base `  c
)  |->  ( x ( Hom  `  c )
y ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  homffval  14651
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