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Definition df-of 5654
Description: Define the function operation map. The definition is designed so that if  R is a binary operation, then  o F 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  o F R  _V ,  _V  |->  dom  i^i  dom  |->  `  R `
Distinct variable group:   ,,, R

Detailed syntax breakdown of Definition df-of
StepHypRef Expression
1 cR . . 3  R
21cof 5652 . 2  o F R
3 vf . . 3  setvar
4 vg . . 3  setvar
5 cvv 2551 . . 3  _V
6 vx . . . 4  setvar
73cv 1241 . . . . . 6
87cdm 4288 . . . . 5  dom
94cv 1241 . . . . . 6
109cdm 4288 . . . . 5  dom
118, 10cin 2910 . . . 4  dom  i^i  dom
126cv 1241 . . . . . 6
1312, 7cfv 4845 . . . . 5  `
1412, 9cfv 4845 . . . . 5  `
1513, 14, 1co 5455 . . . 4  `  R `
166, 11, 15cmpt 3809 . . 3  dom  i^i  dom  |->  `  R `
173, 4, 5, 5, 16cmpt2 5457 . 2  _V ,  _V  |->  dom  i^i  dom  |->  `  R `
182, 17wceq 1242 1  o F R  _V ,  _V  |->  dom  i^i  dom  |->  `  R `
Colors of variables: wff set class
This definition is referenced by:  ofeq  5656  ofexg  5658  offval  5661  offval3  5703  ofmres  5705
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