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Definition df-pprod 24396
Description: Define the parallel product of two classes. Membership in this class is defined by pprodss4v 24424 and brpprod 24425. (Contributed by Scott Fenton, 11-Apr-2014.)
Assertion
Ref Expression
df-pprod  |- pprod ( A ,  B )  =  ( ( A  o.  ( 1st  |`  ( _V  X.  _V ) ) ) 
(x)  ( B  o.  ( 2nd  |`  ( _V  X.  _V ) ) ) )

Detailed syntax breakdown of Definition df-pprod
StepHypRef Expression
1 cA . . 3  class  A
2 cB . . 3  class  B
31, 2cpprod 24374 . 2  class pprod ( A ,  B )
4 c1st 6120 . . . . 5  class  1st
5 cvv 2788 . . . . . 6  class  _V
65, 5cxp 4687 . . . . 5  class  ( _V 
X.  _V )
74, 6cres 4691 . . . 4  class  ( 1st  |`  ( _V  X.  _V ) )
81, 7ccom 4693 . . 3  class  ( A  o.  ( 1st  |`  ( _V  X.  _V ) ) )
9 c2nd 6121 . . . . 5  class  2nd
109, 6cres 4691 . . . 4  class  ( 2nd  |`  ( _V  X.  _V ) )
112, 10ccom 4693 . . 3  class  ( B  o.  ( 2nd  |`  ( _V  X.  _V ) ) )
128, 11ctxp 24373 . 2  class  ( ( A  o.  ( 1st  |`  ( _V  X.  _V ) ) )  (x)  ( B  o.  ( 2nd  |`  ( _V  X.  _V ) ) ) )
133, 12wceq 1623 1  wff pprod ( A ,  B )  =  ( ( A  o.  ( 1st  |`  ( _V  X.  _V ) ) ) 
(x)  ( B  o.  ( 2nd  |`  ( _V  X.  _V ) ) ) )
Colors of variables: wff set class
This definition is referenced by:  dfpprod2  24422  pprodss4v  24424  brpprod  24425
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