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| Mirrors > Home > MPE Home > Th. List > df-pws | Structured version Visualization version GIF version | ||
| Description: Define a structure power, which is just a structure product where all the factors are the same. (Contributed by Mario Carneiro, 11-Jan-2015.) |
| Ref | Expression |
|---|---|
| df-pws | ⊢ ↑s = (𝑟 ∈ V, 𝑖 ∈ V ↦ ((Scalar‘𝑟)Xs(𝑖 × {𝑟}))) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cpws 17491 | . 2 class ↑s | |
| 2 | vr | . . 3 setvar 𝑟 | |
| 3 | vi | . . 3 setvar 𝑖 | |
| 4 | cvv 3480 | . . 3 class V | |
| 5 | 2 | cv 1539 | . . . . 5 class 𝑟 |
| 6 | csca 17300 | . . . . 5 class Scalar | |
| 7 | 5, 6 | cfv 6561 | . . . 4 class (Scalar‘𝑟) |
| 8 | 3 | cv 1539 | . . . . 5 class 𝑖 |
| 9 | 5 | csn 4626 | . . . . 5 class {𝑟} |
| 10 | 8, 9 | cxp 5683 | . . . 4 class (𝑖 × {𝑟}) |
| 11 | cprds 17490 | . . . 4 class Xs | |
| 12 | 7, 10, 11 | co 7431 | . . 3 class ((Scalar‘𝑟)Xs(𝑖 × {𝑟})) |
| 13 | 2, 3, 4, 4, 12 | cmpo 7433 | . 2 class (𝑟 ∈ V, 𝑖 ∈ V ↦ ((Scalar‘𝑟)Xs(𝑖 × {𝑟}))) |
| 14 | 1, 13 | wceq 1540 | 1 wff ↑s = (𝑟 ∈ V, 𝑖 ∈ V ↦ ((Scalar‘𝑟)Xs(𝑖 × {𝑟}))) |
| Colors of variables: wff setvar class |
| This definition is referenced by: pwsval 17531 |
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