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Definition df-cap 24411
Description: Define the little cap function. See brcap 24479 for its value. (Contributed by Scott Fenton, 17-Apr-2014.)
Assertion
Ref Expression
df-cap  |- Cap  =  ( ( ( _V  X.  _V )  X.  _V )  \  ran  ( ( _V 
(x)  _E  )(++) (
( ( `' 1st  o.  _E  )  i^i  ( `' 2nd  o.  _E  )
)  (x)  _V )
) )

Detailed syntax breakdown of Definition df-cap
StepHypRef Expression
1 ccap 24390 . 2  class Cap
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  )
7 c1st 6120 . . . . . . . . 9  class  1st
87ccnv 4688 . . . . . . . 8  class  `' 1st
98, 5ccom 4693 . . . . . . 7  class  ( `' 1st  o.  _E  )
10 c2nd 6121 . . . . . . . . 9  class  2nd
1110ccnv 4688 . . . . . . . 8  class  `' 2nd
1211, 5ccom 4693 . . . . . . 7  class  ( `' 2nd  o.  _E  )
139, 12cin 3151 . . . . . 6  class  ( ( `' 1st  o.  _E  )  i^i  ( `' 2nd  o.  _E  ) )
1413, 2ctxp 24373 . . . . 5  class  ( ( ( `' 1st  o.  _E  )  i^i  ( `' 2nd  o.  _E  )
)  (x)  _V )
156, 14csymdif 24361 . . . 4  class  ( ( _V  (x)  _E  )(++) ( ( ( `' 1st  o.  _E  )  i^i  ( `' 2nd  o.  _E  ) )  (x)  _V ) )
1615crn 4690 . . 3  class  ran  (
( _V  (x)  _E  )(++) ( ( ( `' 1st  o.  _E  )  i^i  ( `' 2nd  o.  _E  ) )  (x)  _V ) )
174, 16cdif 3149 . 2  class  ( ( ( _V  X.  _V )  X.  _V )  \  ran  ( ( _V  (x)  _E  )(++) ( ( ( `' 1st  o.  _E  )  i^i  ( `' 2nd  o.  _E  ) )  (x)  _V ) ) )
181, 17wceq 1623 1  wff Cap  =  ( ( ( _V  X.  _V )  X.  _V )  \  ran  ( ( _V 
(x)  _E  )(++) (
( ( `' 1st  o.  _E  )  i^i  ( `' 2nd  o.  _E  )
)  (x)  _V )
) )
Colors of variables: wff set class
This definition is referenced by:  brcap  24479
  Copyright terms: Public domain W3C validator