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Definition df-funs 24402
Description: Define the class of all functions. See elfuns 24454 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 24380 . 2  class  Funs
2 cvv 2788 . . . . 5  class  _V
32, 2cxp 4687 . . . 4  class  ( _V 
X.  _V )
43cpw 3625 . . 3  class  ~P ( _V  X.  _V )
5 cep 4303 . . . . 5  class  _E
6 c1st 6120 . . . . . . 7  class  1st
7 cid 4304 . . . . . . . . 9  class  _I
82, 7cdif 3149 . . . . . . . 8  class  ( _V 
\  _I  )
9 c2nd 6121 . . . . . . . 8  class  2nd
108, 9ccom 4693 . . . . . . 7  class  ( ( _V  \  _I  )  o.  2nd )
116, 10ctxp 24373 . . . . . 6  class  ( 1st  (x)  ( ( _V  \  _I  )  o.  2nd ) )
125ccnv 4688 . . . . . 6  class  `'  _E
1311, 12ccom 4693 . . . . 5  class  ( ( 1st  (x)  ( ( _V  \  _I  )  o. 
2nd ) )  o.  `'  _E  )
145, 13ccom 4693 . . . 4  class  (  _E  o.  ( ( 1st  (x)  ( ( _V  \  _I  )  o.  2nd ) )  o.  `'  _E  ) )
1514cfix 24378 . . 3  class  Fix (  _E  o.  ( ( 1st  (x)  ( ( _V  \  _I  )  o.  2nd ) )  o.  `'  _E  ) )
164, 15cdif 3149 . 2  class  ( ~P ( _V  X.  _V )  \  Fix (  _E  o.  ( ( 1st  (x)  ( ( _V  \  _I  )  o.  2nd ) )  o.  `'  _E  ) ) )
171, 16wceq 1623 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  24454
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