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Definition df-subr 27659
Description: Define the operation of vector subtraction. (Contributed by Andrew Salmon, 27-Jan-2012.)
Assertion
Ref Expression
df-subr  |-  - r  =  ( x  e. 
_V ,  y  e. 
_V  |->  ( v  e.  RR  |->  ( ( x `
 v )  -  ( y `  v
) ) ) )
Distinct variable group:    x, v, y

Detailed syntax breakdown of Definition df-subr
StepHypRef Expression
1 cminusr 27653 . 2  class  - r
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cvv 2958 . . 3  class  _V
5 vv . . . 4  set  v
6 cr 8994 . . . 4  class  RR
75cv 1652 . . . . . 6  class  v
82cv 1652 . . . . . 6  class  x
97, 8cfv 5457 . . . . 5  class  ( x `
 v )
103cv 1652 . . . . . 6  class  y
117, 10cfv 5457 . . . . 5  class  ( y `
 v )
12 cmin 9296 . . . . 5  class  -
139, 11, 12co 6084 . . . 4  class  ( ( x `  v )  -  ( y `  v ) )
145, 6, 13cmpt 4269 . . 3  class  ( v  e.  RR  |->  ( ( x `  v )  -  ( y `  v ) ) )
152, 3, 4, 4, 14cmpt2 6086 . 2  class  ( x  e.  _V ,  y  e.  _V  |->  ( v  e.  RR  |->  ( ( x `  v )  -  ( y `  v ) ) ) )
161, 15wceq 1653 1  wff  - r  =  ( x  e. 
_V ,  y  e. 
_V  |->  ( v  e.  RR  |->  ( ( x `
 v )  -  ( y `  v
) ) ) )
Colors of variables: wff set class
This definition is referenced by:  subrval  27662
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