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Definition df-sx 32455
Description: Define the product sigma-algebra operation, analogous to df-tx 22819. (Contributed by Thierry Arnoux, 1-Jun-2017.)
Assertion
Ref Expression
df-sx Γ—s = (𝑠 ∈ V, 𝑑 ∈ V ↦ (sigaGenβ€˜ran (π‘₯ ∈ 𝑠, 𝑦 ∈ 𝑑 ↦ (π‘₯ Γ— 𝑦))))
Distinct variable group:   𝑑,𝑠,π‘₯,𝑦

Detailed syntax breakdown of Definition df-sx
StepHypRef Expression
1 csx 32454 . 2 class Γ—s
2 vs . . 3 setvar 𝑠
3 vt . . 3 setvar 𝑑
4 cvv 3441 . . 3 class V
5 vx . . . . . 6 setvar π‘₯
6 vy . . . . . 6 setvar 𝑦
72cv 1539 . . . . . 6 class 𝑠
83cv 1539 . . . . . 6 class 𝑑
95cv 1539 . . . . . . 7 class π‘₯
106cv 1539 . . . . . . 7 class 𝑦
119, 10cxp 5618 . . . . . 6 class (π‘₯ Γ— 𝑦)
125, 6, 7, 8, 11cmpo 7339 . . . . 5 class (π‘₯ ∈ 𝑠, 𝑦 ∈ 𝑑 ↦ (π‘₯ Γ— 𝑦))
1312crn 5621 . . . 4 class ran (π‘₯ ∈ 𝑠, 𝑦 ∈ 𝑑 ↦ (π‘₯ Γ— 𝑦))
14 csigagen 32404 . . . 4 class sigaGen
1513, 14cfv 6479 . . 3 class (sigaGenβ€˜ran (π‘₯ ∈ 𝑠, 𝑦 ∈ 𝑑 ↦ (π‘₯ Γ— 𝑦)))
162, 3, 4, 4, 15cmpo 7339 . 2 class (𝑠 ∈ V, 𝑑 ∈ V ↦ (sigaGenβ€˜ran (π‘₯ ∈ 𝑠, 𝑦 ∈ 𝑑 ↦ (π‘₯ Γ— 𝑦))))
171, 16wceq 1540 1 wff Γ—s = (𝑠 ∈ V, 𝑑 ∈ V ↦ (sigaGenβ€˜ran (π‘₯ ∈ 𝑠, 𝑦 ∈ 𝑑 ↦ (π‘₯ Γ— 𝑦))))
Colors of variables: wff setvar class
This definition is referenced by:  sxval  32456
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