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Definition df-cart 24406
Description: Define the cartesian product function. See brcart 24471 for its value. (Contributed by Scott Fenton, 11-Apr-2014.)
Assertion
Ref Expression
df-cart  |- Cart  =  ( ( ( _V  X.  _V )  X.  _V )  \  ran  ( ( _V 
(x)  _E  )(++) (pprod (  _E  ,  _E  )  (x)  _V ) ) )

Detailed syntax breakdown of Definition df-cart
StepHypRef Expression
1 ccart 24384 . 2  class Cart
2 cvv 2788 . . . . 5  class  _V
32, 2cxp 4687 . . . 4  class  ( _V 
X.  _V )
43, 2cxp 4687 . . 3  class  ( ( _V  X.  _V )  X.  _V )
5 cep 4303 . . . . . 6  class  _E
62, 5ctxp 24373 . . . . 5  class  ( _V 
(x)  _E  )
75, 5cpprod 24374 . . . . . 6  class pprod (  _E  ,  _E  )
87, 2ctxp 24373 . . . . 5  class  (pprod (  _E  ,  _E  )  (x)  _V )
96, 8csymdif 24361 . . . 4  class  ( ( _V  (x)  _E  )(++) (pprod (  _E  ,  _E  )  (x)  _V ) )
109crn 4690 . . 3  class  ran  (
( _V  (x)  _E  )(++) (pprod (  _E  ,  _E  )  (x)  _V )
)
114, 10cdif 3149 . 2  class  ( ( ( _V  X.  _V )  X.  _V )  \  ran  ( ( _V  (x)  _E  )(++) (pprod (  _E  ,  _E  )  (x)  _V ) ) )
121, 11wceq 1623 1  wff Cart  =  ( ( ( _V  X.  _V )  X.  _V )  \  ran  ( ( _V 
(x)  _E  )(++) (pprod (  _E  ,  _E  )  (x)  _V ) ) )
Colors of variables: wff set class
This definition is referenced by:  brcart  24471
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