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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-bj-rrvec | Structured version Visualization version GIF version |
Description: Definition of the class of real vector spaces. (Contributed by BJ, 9-Jun-2019.) |
Ref | Expression |
---|---|
df-bj-rrvec | ⊢ ℝ-Vec = {𝑥 ∈ LVec ∣ (Scalar‘𝑥) = ℝfld} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | crrvec 32325 | . 2 class ℝ-Vec | |
2 | vx | . . . . . 6 setvar 𝑥 | |
3 | 2 | cv 1474 | . . . . 5 class 𝑥 |
4 | csca 15771 | . . . . 5 class Scalar | |
5 | 3, 4 | cfv 5804 | . . . 4 class (Scalar‘𝑥) |
6 | crefld 19769 | . . . 4 class ℝfld | |
7 | 5, 6 | wceq 1475 | . . 3 wff (Scalar‘𝑥) = ℝfld |
8 | clvec 18923 | . . 3 class LVec | |
9 | 7, 2, 8 | crab 2900 | . 2 class {𝑥 ∈ LVec ∣ (Scalar‘𝑥) = ℝfld} |
10 | 1, 9 | wceq 1475 | 1 wff ℝ-Vec = {𝑥 ∈ LVec ∣ (Scalar‘𝑥) = ℝfld} |
Colors of variables: wff setvar class |
This definition is referenced by: bj-rrvecssvec 32327 |
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