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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 16951 | . 2 class ↑s | |
2 | vr | . . 3 setvar 𝑟 | |
3 | vi | . . 3 setvar 𝑖 | |
4 | cvv 3408 | . . 3 class V | |
5 | 2 | cv 1542 | . . . . 5 class 𝑟 |
6 | csca 16805 | . . . . 5 class Scalar | |
7 | 5, 6 | cfv 6380 | . . . 4 class (Scalar‘𝑟) |
8 | 3 | cv 1542 | . . . . 5 class 𝑖 |
9 | 5 | csn 4541 | . . . . 5 class {𝑟} |
10 | 8, 9 | cxp 5549 | . . . 4 class (𝑖 × {𝑟}) |
11 | cprds 16950 | . . . 4 class Xs | |
12 | 7, 10, 11 | co 7213 | . . 3 class ((Scalar‘𝑟)Xs(𝑖 × {𝑟})) |
13 | 2, 3, 4, 4, 12 | cmpo 7215 | . 2 class (𝑟 ∈ V, 𝑖 ∈ V ↦ ((Scalar‘𝑟)Xs(𝑖 × {𝑟}))) |
14 | 1, 13 | wceq 1543 | 1 wff ↑s = (𝑟 ∈ V, 𝑖 ∈ V ↦ ((Scalar‘𝑟)Xs(𝑖 × {𝑟}))) |
Colors of variables: wff setvar class |
This definition is referenced by: pwsval 16991 |
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