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Definition df-sx 30561
 Description: Define the product sigma-algebra operation, analogous to df-tx 21567. (Contributed by Thierry Arnoux, 1-Jun-2017.)
Assertion
Ref Expression
df-sx ×s = (𝑠 ∈ V, 𝑡 ∈ V ↦ (sigaGen‘ran (𝑥𝑠, 𝑦𝑡 ↦ (𝑥 × 𝑦))))
Distinct variable group:   𝑡,𝑠,𝑥,𝑦

Detailed syntax breakdown of Definition df-sx
StepHypRef Expression
1 csx 30560 . 2 class ×s
2 vs . . 3 setvar 𝑠
3 vt . . 3 setvar 𝑡
4 cvv 3340 . . 3 class V
5 vx . . . . . 6 setvar 𝑥
6 vy . . . . . 6 setvar 𝑦
72cv 1631 . . . . . 6 class 𝑠
83cv 1631 . . . . . 6 class 𝑡
95cv 1631 . . . . . . 7 class 𝑥
106cv 1631 . . . . . . 7 class 𝑦
119, 10cxp 5264 . . . . . 6 class (𝑥 × 𝑦)
125, 6, 7, 8, 11cmpt2 6815 . . . . 5 class (𝑥𝑠, 𝑦𝑡 ↦ (𝑥 × 𝑦))
1312crn 5267 . . . 4 class ran (𝑥𝑠, 𝑦𝑡 ↦ (𝑥 × 𝑦))
14 csigagen 30510 . . . 4 class sigaGen
1513, 14cfv 6049 . . 3 class (sigaGen‘ran (𝑥𝑠, 𝑦𝑡 ↦ (𝑥 × 𝑦)))
162, 3, 4, 4, 15cmpt2 6815 . 2 class (𝑠 ∈ V, 𝑡 ∈ V ↦ (sigaGen‘ran (𝑥𝑠, 𝑦𝑡 ↦ (𝑥 × 𝑦))))
171, 16wceq 1632 1 wff ×s = (𝑠 ∈ V, 𝑡 ∈ V ↦ (sigaGen‘ran (𝑥𝑠, 𝑦𝑡 ↦ (𝑥 × 𝑦))))
 Colors of variables: wff setvar class This definition is referenced by:  sxval  30562
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