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Definition df-mod 11243
Description: Define the modulo (remainder) operation. See modval 11244 for its value. (Contributed by NM, 10-Nov-2008.)
Assertion
Ref Expression
df-mod  |-  mod  =  ( x  e.  RR ,  y  e.  RR+  |->  ( x  -  ( y  x.  ( |_ `  (
x  /  y ) ) ) ) )
Distinct variable group:    x, y

Detailed syntax breakdown of Definition df-mod
StepHypRef Expression
1 cmo 11242 . 2  class  mod
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cr 8981 . . 3  class  RR
5 crp 10604 . . 3  class  RR+
62cv 1651 . . . 4  class  x
73cv 1651 . . . . 5  class  y
8 cdiv 9669 . . . . . . 7  class  /
96, 7, 8co 6073 . . . . . 6  class  ( x  /  y )
10 cfl 11193 . . . . . 6  class  |_
119, 10cfv 5446 . . . . 5  class  ( |_
`  ( x  / 
y ) )
12 cmul 8987 . . . . 5  class  x.
137, 11, 12co 6073 . . . 4  class  ( y  x.  ( |_ `  ( x  /  y
) ) )
14 cmin 9283 . . . 4  class  -
156, 13, 14co 6073 . . 3  class  ( x  -  ( y  x.  ( |_ `  (
x  /  y ) ) ) )
162, 3, 4, 5, 15cmpt2 6075 . 2  class  ( x  e.  RR ,  y  e.  RR+  |->  ( x  -  ( y  x.  ( |_ `  (
x  /  y ) ) ) ) )
171, 16wceq 1652 1  wff  mod  =  ( x  e.  RR ,  y  e.  RR+  |->  ( x  -  ( y  x.  ( |_ `  (
x  /  y ) ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  modval  11244
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