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Definition df-addr 27771
Description: Define the operation of vector addition. (Contributed by Andrew Salmon, 27-Jan-2012.)
Assertion
Ref Expression
df-addr  |-  + 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-addr
StepHypRef Expression
1 cplusr 27765 . 2  class  + r
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cvv 2801 . . 3  class  _V
5 vv . . . 4  set  v
6 cr 8752 . . . 4  class  RR
75cv 1631 . . . . . 6  class  v
82cv 1631 . . . . . 6  class  x
97, 8cfv 5271 . . . . 5  class  ( x `
 v )
103cv 1631 . . . . . 6  class  y
117, 10cfv 5271 . . . . 5  class  ( y `
 v )
12 caddc 8756 . . . . 5  class  +
139, 11, 12co 5874 . . . 4  class  ( ( x `  v )  +  ( y `  v ) )
145, 6, 13cmpt 4093 . . 3  class  ( v  e.  RR  |->  ( ( x `  v )  +  ( y `  v ) ) )
152, 3, 4, 4, 14cmpt2 5876 . 2  class  ( x  e.  _V ,  y  e.  _V  |->  ( v  e.  RR  |->  ( ( x `  v )  +  ( y `  v ) ) ) )
161, 15wceq 1632 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:  addrval  27774
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