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Definition df-mulv 27670
Description: Define the operation of scalar multiplication. (Contributed by Andrew Salmon, 27-Jan-2012.)
Assertion
Ref Expression
df-mulv  |-  . v  =  ( x  e. 
_V ,  y  e. 
_V  |->  ( v  e.  RR  |->  ( x  x.  ( y `  v
) ) ) )
Distinct variable group:    x, v, y

Detailed syntax breakdown of Definition df-mulv
StepHypRef Expression
1 ctimesr 27664 . 2  class  . v
2 vx . . 3  set  x
3 vy . . 3  set  y
4 cvv 2788 . . 3  class  _V
5 vv . . . 4  set  v
6 cr 8736 . . . 4  class  RR
72cv 1622 . . . . 5  class  x
85cv 1622 . . . . . 6  class  v
93cv 1622 . . . . . 6  class  y
108, 9cfv 5255 . . . . 5  class  ( y `
 v )
11 cmul 8742 . . . . 5  class  x.
127, 10, 11co 5858 . . . 4  class  ( x  x.  ( y `  v ) )
135, 6, 12cmpt 4077 . . 3  class  ( v  e.  RR  |->  ( x  x.  ( y `  v ) ) )
142, 3, 4, 4, 13cmpt2 5860 . 2  class  ( x  e.  _V ,  y  e.  _V  |->  ( v  e.  RR  |->  ( x  x.  ( y `  v ) ) ) )
151, 14wceq 1623 1  wff  . v  =  ( x  e. 
_V ,  y  e. 
_V  |->  ( v  e.  RR  |->  ( x  x.  ( y `  v
) ) ) )
Colors of variables: wff set class
This definition is referenced by:  mulvval  27673
  Copyright terms: Public domain W3C validator