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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-rr3 | Structured version Visualization version GIF version |
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 |
---|---|
df-rr3 | ⊢ RR3 = (ℝ ↑𝑚 {1, 2, 3}) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | crr3c 37686 | . 2 class RR3 | |
2 | cr 9814 | . . 3 class ℝ | |
3 | c1 9816 | . . . 4 class 1 | |
4 | c2 10947 | . . . 4 class 2 | |
5 | c3 10948 | . . . 4 class 3 | |
6 | 3, 4, 5 | ctp 4129 | . . 3 class {1, 2, 3} |
7 | cmap 7744 | . . 3 class ↑𝑚 | |
8 | 2, 6, 7 | co 6549 | . 2 class (ℝ ↑𝑚 {1, 2, 3}) |
9 | 1, 8 | wceq 1475 | 1 wff RR3 = (ℝ ↑𝑚 {1, 2, 3}) |
Colors of variables: wff setvar class |
This definition is referenced by: (None) |
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