Definition df-mulv 38669

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

Step	Hyp	Ref	Expression
1		ctimesr 38663	. 2 class .v
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		cvv 3200	. . 3 class _V
5		vv	. . . 4 setvar v
6		cr 9935	. . . 4 class RR
7	2	cv 1482	. . . . 5 class x
8	5	cv 1482	. . . . . 6 class v
9	3	cv 1482	. . . . . 6 class y
10	8, 9	cfv 5888	. . . . 5 class ( y ` v )
11		cmul 9941	. . . . 5 class x.
12	7, 10, 11	co 6650	. . . 4 class ( x x. ( y ` v ) )
13	5, 6, 12	cmpt 4729	. . 3 class ( v e. RR |-> ( x x. ( y ` v ) ) )
14	2, 3, 4, 4, 13	cmpt2 6652	. 2 class ( x e. _V , y e. _V |-> ( v e. RR |-> ( x x. ( y ` v ) ) ) )
15	1, 14	wceq 1483	1 wff .v = ( x e. _V , y e. _V |-> ( v e. RR |-> ( x x. ( y ` v ) ) ) )

This definition is referenced by:  mulvval  38672