MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-tx Structured version   Visualization version   GIF version

Definition df-tx 23066
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 Γ—t = (π‘Ÿ ∈ V, 𝑠 ∈ V ↦ (topGenβ€˜ran (π‘₯ ∈ π‘Ÿ, 𝑦 ∈ 𝑠 ↦ (π‘₯ Γ— 𝑦))))
Distinct variable group:   𝑠,π‘Ÿ,π‘₯,𝑦

Detailed syntax breakdown of Definition df-tx
StepHypRef Expression
1 ctx 23064 . 2 class Γ—t
2 vr . . 3 setvar π‘Ÿ
3 vs . . 3 setvar 𝑠
4 cvv 3475 . . 3 class V
5 vx . . . . . 6 setvar π‘₯
6 vy . . . . . 6 setvar 𝑦
72cv 1541 . . . . . 6 class π‘Ÿ
83cv 1541 . . . . . 6 class 𝑠
95cv 1541 . . . . . . 7 class π‘₯
106cv 1541 . . . . . . 7 class 𝑦
119, 10cxp 5675 . . . . . 6 class (π‘₯ Γ— 𝑦)
125, 6, 7, 8, 11cmpo 7411 . . . . 5 class (π‘₯ ∈ π‘Ÿ, 𝑦 ∈ 𝑠 ↦ (π‘₯ Γ— 𝑦))
1312crn 5678 . . . 4 class ran (π‘₯ ∈ π‘Ÿ, 𝑦 ∈ 𝑠 ↦ (π‘₯ Γ— 𝑦))
14 ctg 17383 . . . 4 class topGen
1513, 14cfv 6544 . . 3 class (topGenβ€˜ran (π‘₯ ∈ π‘Ÿ, 𝑦 ∈ 𝑠 ↦ (π‘₯ Γ— 𝑦)))
162, 3, 4, 4, 15cmpo 7411 . 2 class (π‘Ÿ ∈ V, 𝑠 ∈ V ↦ (topGenβ€˜ran (π‘₯ ∈ π‘Ÿ, 𝑦 ∈ 𝑠 ↦ (π‘₯ Γ— 𝑦))))
171, 16wceq 1542 1 wff Γ—t = (π‘Ÿ ∈ V, 𝑠 ∈ V ↦ (topGenβ€˜ran (π‘₯ ∈ π‘Ÿ, 𝑦 ∈ 𝑠 ↦ (π‘₯ Γ— 𝑦))))
Colors of variables: wff setvar class
This definition is referenced by:  txval  23068
  Copyright terms: Public domain W3C validator