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Definition df-pws 16157
 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.)
Assertion
Ref Expression
df-pws s = (𝑟 ∈ V, 𝑖 ∈ V ↦ ((Scalar‘𝑟)Xs(𝑖 × {𝑟})))
Distinct variable group:   𝑖,𝑟

Detailed syntax breakdown of Definition df-pws
StepHypRef Expression
1 cpws 16154 . 2 class s
2 vr . . 3 setvar 𝑟
3 vi . . 3 setvar 𝑖
4 cvv 3231 . . 3 class V
52cv 1522 . . . . 5 class 𝑟
6 csca 15991 . . . . 5 class Scalar
75, 6cfv 5926 . . . 4 class (Scalar‘𝑟)
83cv 1522 . . . . 5 class 𝑖
95csn 4210 . . . . 5 class {𝑟}
108, 9cxp 5141 . . . 4 class (𝑖 × {𝑟})
11 cprds 16153 . . . 4 class Xs
127, 10, 11co 6690 . . 3 class ((Scalar‘𝑟)Xs(𝑖 × {𝑟}))
132, 3, 4, 4, 12cmpt2 6692 . 2 class (𝑟 ∈ V, 𝑖 ∈ V ↦ ((Scalar‘𝑟)Xs(𝑖 × {𝑟})))
141, 13wceq 1523 1 wff s = (𝑟 ∈ V, 𝑖 ∈ V ↦ ((Scalar‘𝑟)Xs(𝑖 × {𝑟})))
 Colors of variables: wff setvar class This definition is referenced by:  pwsval  16193
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