Definition df-rr3

Description: Define the set of all points RR3 . We define each point A as a function to allow the use of vector addition and subtraction as well as scalar multiplication in our proofs. (Contributed by Andrew Salmon, 15-Jul-2012)

	Ref	Expression
Assertion	df-rr3	$$⊢\mathrm{RR3}={ℝ}^{\left\{1,2,3\right\}}$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		crr3c	$$class\mathrm{RR3}$$
1		cr	$$classℝ$$
2		cmap	$$class{\uparrow }_{𝑚}$$
3		c1	$$class1$$
4		c2	$$class2$$
5		c3	$$class3$$
6	3 4 5	ctp	$$class\left\{1,2,3\right\}$$
7	1 6 2	co	$$class\left({ℝ}^{\left\{1,2,3\right\}}\right)$$
8	0 7	wceq	$$wff\mathrm{RR3}={ℝ}^{\left\{1,2,3\right\}}$$