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Definition df-tx 17273
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  |-  tX  =  ( r  e.  _V ,  s  e.  _V  |->  ( topGen `  ran  ( x  e.  r ,  y  e.  s  |->  ( x  X.  y ) ) ) )
Distinct variable group:    s, r, x, y

Detailed syntax breakdown of Definition df-tx
StepHypRef Expression
1 ctx 17271 . 2  class  tX
2 vr . . 3  set  r
3 vs . . 3  set  s
4 cvv 2801 . . 3  class  _V
5 vx . . . . . 6  set  x
6 vy . . . . . 6  set  y
72cv 1631 . . . . . 6  class  r
83cv 1631 . . . . . 6  class  s
95cv 1631 . . . . . . 7  class  x
106cv 1631 . . . . . . 7  class  y
119, 10cxp 4703 . . . . . 6  class  ( x  X.  y )
125, 6, 7, 8, 11cmpt2 5876 . . . . 5  class  ( x  e.  r ,  y  e.  s  |->  ( x  X.  y ) )
1312crn 4706 . . . 4  class  ran  (
x  e.  r ,  y  e.  s  |->  ( x  X.  y ) )
14 ctg 13358 . . . 4  class  topGen
1513, 14cfv 5271 . . 3  class  ( topGen ` 
ran  ( x  e.  r ,  y  e.  s  |->  ( x  X.  y ) ) )
162, 3, 4, 4, 15cmpt2 5876 . 2  class  ( r  e.  _V ,  s  e.  _V  |->  ( topGen ` 
ran  ( x  e.  r ,  y  e.  s  |->  ( x  X.  y ) ) ) )
171, 16wceq 1632 1  wff  tX  =  ( r  e.  _V ,  s  e.  _V  |->  ( topGen `  ran  ( x  e.  r ,  y  e.  s  |->  ( x  X.  y ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  txval  17275
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