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Definition df-mod 12094
Description: Define the modulo (remainder) operation. See modval 12095 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 12093 . 2  class  mod
2 vx . . 3  setvar  x
3 vy . . 3  setvar  y
4 cr 9537 . . 3  class  RR
5 crp 11302 . . 3  class  RR+
62cv 1436 . . . 4  class  x
73cv 1436 . . . . 5  class  y
8 cdiv 10268 . . . . . . 7  class  /
96, 7, 8co 6305 . . . . . 6  class  ( x  /  y )
10 cfl 12023 . . . . . 6  class  |_
119, 10cfv 5601 . . . . 5  class  ( |_
`  ( x  / 
y ) )
12 cmul 9543 . . . . 5  class  x.
137, 11, 12co 6305 . . . 4  class  ( y  x.  ( |_ `  ( x  /  y
) ) )
14 cmin 9859 . . . 4  class  -
156, 13, 14co 6305 . . 3  class  ( x  -  ( y  x.  ( |_ `  (
x  /  y ) ) ) )
162, 3, 4, 5, 15cmpt2 6307 . 2  class  ( x  e.  RR ,  y  e.  RR+  |->  ( x  -  ( y  x.  ( |_ `  (
x  /  y ) ) ) ) )
171, 16wceq 1437 1  wff  mod  =  ( x  e.  RR ,  y  e.  RR+  |->  ( x  -  ( y  x.  ( |_ `  (
x  /  y ) ) ) ) )
Colors of variables: wff setvar class
This definition is referenced by:  modval  12095
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