Definition df-subr 38668

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

Step	Hyp	Ref	Expression
1		cminusr 38662	. 2 class -r
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	5	cv 1482	. . . . . 6 class v
8	2	cv 1482	. . . . . 6 class x
9	7, 8	cfv 5888	. . . . 5 class ( x ` v )
10	3	cv 1482	. . . . . 6 class y
11	7, 10	cfv 5888	. . . . 5 class ( y ` v )
12		cmin 10266	. . . . 5 class -
13	9, 11, 12	co 6650	. . . 4 class ( ( x ` v ) - ( y ` v ) )
14	5, 6, 13	cmpt 4729	. . 3 class ( v e. RR |-> ( ( x ` v ) - ( y ` v ) ) )
15	2, 3, 4, 4, 14	cmpt2 6652	. 2 class ( x e. _V , y e. _V |-> ( v e. RR |-> ( ( x ` v ) - ( y ` v ) ) ) )
16	1, 15	wceq 1483	1 wff -r = ( x e. _V , y e. _V |-> ( v e. RR |-> ( ( x ` v ) - ( y ` v ) ) ) )

This definition is referenced by:  subrval  38671