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Definition df-of 5743
Description: Define the function operation map. The definition is designed so that if  R is a binary operation, then  oF R is the analogous operation on functions which corresponds to applying  R pointwise to the values of the functions. (Contributed by Mario Carneiro, 20-Jul-2014.)
Assertion
Ref Expression
df-of  |-  oF R  =  ( f  e.  _V ,  g  e.  _V  |->  ( x  e.  ( dom  f  i^i  dom  g )  |->  ( ( f `  x
) R ( g `
 x ) ) ) )
Distinct variable group:    f, g, x, R

Detailed syntax breakdown of Definition df-of
StepHypRef Expression
1 cR . . 3  class  R
21cof 5741 . 2  class  oF R
3 vf . . 3  setvar  f
4 vg . . 3  setvar  g
5 cvv 2602 . . 3  class  _V
6 vx . . . 4  setvar  x
73cv 1284 . . . . . 6  class  f
87cdm 4371 . . . . 5  class  dom  f
94cv 1284 . . . . . 6  class  g
109cdm 4371 . . . . 5  class  dom  g
118, 10cin 2973 . . . 4  class  ( dom  f  i^i  dom  g
)
126cv 1284 . . . . . 6  class  x
1312, 7cfv 4932 . . . . 5  class  ( f `
 x )
1412, 9cfv 4932 . . . . 5  class  ( g `
 x )
1513, 14, 1co 5543 . . . 4  class  ( ( f `  x ) R ( g `  x ) )
166, 11, 15cmpt 3847 . . 3  class  ( x  e.  ( dom  f  i^i  dom  g )  |->  ( ( f `  x
) R ( g `
 x ) ) )
173, 4, 5, 5, 16cmpt2 5545 . 2  class  ( f  e.  _V ,  g  e.  _V  |->  ( x  e.  ( dom  f  i^i  dom  g )  |->  ( ( f `  x
) R ( g `
 x ) ) ) )
182, 17wceq 1285 1  wff  oF R  =  ( f  e.  _V ,  g  e.  _V  |->  ( x  e.  ( dom  f  i^i  dom  g )  |->  ( ( f `  x
) R ( g `
 x ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  ofeq  5745  ofexg  5747  offval  5750  offval3  5792  ofmres  5794
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