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Definition df-funs 25419
Description: Define the class of all functions. See elfuns 25471 for membership. (Contributed by Scott Fenton, 18-Feb-2013.)
Assertion
Ref Expression
df-funs  |-  Funs  =  ( ~P ( _V  X.  _V )  \  Fix (  _E  o.  ( ( 1st  (x)  ( ( _V  \  _I  )  o.  2nd ) )  o.  `'  _E  ) ) )

Detailed syntax breakdown of Definition df-funs
StepHypRef Expression
1 cfuns 25397 . 2  class  Funs
2 cvv 2892 . . . . 5  class  _V
32, 2cxp 4809 . . . 4  class  ( _V 
X.  _V )
43cpw 3735 . . 3  class  ~P ( _V  X.  _V )
5 cep 4426 . . . . 5  class  _E
6 c1st 6279 . . . . . . 7  class  1st
7 cid 4427 . . . . . . . . 9  class  _I
82, 7cdif 3253 . . . . . . . 8  class  ( _V 
\  _I  )
9 c2nd 6280 . . . . . . . 8  class  2nd
108, 9ccom 4815 . . . . . . 7  class  ( ( _V  \  _I  )  o.  2nd )
116, 10ctxp 25390 . . . . . 6  class  ( 1st  (x)  ( ( _V  \  _I  )  o.  2nd ) )
125ccnv 4810 . . . . . 6  class  `'  _E
1311, 12ccom 4815 . . . . 5  class  ( ( 1st  (x)  ( ( _V  \  _I  )  o. 
2nd ) )  o.  `'  _E  )
145, 13ccom 4815 . . . 4  class  (  _E  o.  ( ( 1st  (x)  ( ( _V  \  _I  )  o.  2nd ) )  o.  `'  _E  ) )
1514cfix 25395 . . 3  class  Fix (  _E  o.  ( ( 1st  (x)  ( ( _V  \  _I  )  o.  2nd ) )  o.  `'  _E  ) )
164, 15cdif 3253 . 2  class  ( ~P ( _V  X.  _V )  \  Fix (  _E  o.  ( ( 1st  (x)  ( ( _V  \  _I  )  o.  2nd ) )  o.  `'  _E  ) ) )
171, 16wceq 1649 1  wff  Funs  =  ( ~P ( _V  X.  _V )  \  Fix (  _E  o.  ( ( 1st  (x)  ( ( _V  \  _I  )  o.  2nd ) )  o.  `'  _E  ) ) )
Colors of variables: wff set class
This definition is referenced by:  elfuns  25471
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