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Definition df-tx 21579
Description: Define the binary topological product, which is homeomorphic to the general topological product over a two element set, but is more convenient to use. (Contributed by Jeff Madsen, 2-Sep-2009.)
Assertion
Ref Expression
df-tx ×t = (𝑟 ∈ V, 𝑠 ∈ V ↦ (topGen‘ran (𝑥𝑟, 𝑦𝑠 ↦ (𝑥 × 𝑦))))
Distinct variable group:   𝑠,𝑟,𝑥,𝑦

Detailed syntax breakdown of Definition df-tx
StepHypRef Expression
1 ctx 21577 . 2 class ×t
2 vr . . 3 setvar 𝑟
3 vs . . 3 setvar 𝑠
4 cvv 3391 . . 3 class V
5 vx . . . . . 6 setvar 𝑥
6 vy . . . . . 6 setvar 𝑦
72cv 1636 . . . . . 6 class 𝑟
83cv 1636 . . . . . 6 class 𝑠
95cv 1636 . . . . . . 7 class 𝑥
106cv 1636 . . . . . . 7 class 𝑦
119, 10cxp 5309 . . . . . 6 class (𝑥 × 𝑦)
125, 6, 7, 8, 11cmpt2 6876 . . . . 5 class (𝑥𝑟, 𝑦𝑠 ↦ (𝑥 × 𝑦))
1312crn 5312 . . . 4 class ran (𝑥𝑟, 𝑦𝑠 ↦ (𝑥 × 𝑦))
14 ctg 16303 . . . 4 class topGen
1513, 14cfv 6101 . . 3 class (topGen‘ran (𝑥𝑟, 𝑦𝑠 ↦ (𝑥 × 𝑦)))
162, 3, 4, 4, 15cmpt2 6876 . 2 class (𝑟 ∈ V, 𝑠 ∈ V ↦ (topGen‘ran (𝑥𝑟, 𝑦𝑠 ↦ (𝑥 × 𝑦))))
171, 16wceq 1637 1 wff ×t = (𝑟 ∈ V, 𝑠 ∈ V ↦ (topGen‘ran (𝑥𝑟, 𝑦𝑠 ↦ (𝑥 × 𝑦))))
Colors of variables: wff setvar class
This definition is referenced by:  txval  21581
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