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Definition df-dfat 27974
Description: Definition of the predicate that determines if some class  F is defined as function for an argument  A or, in other words, if the function value for some class  F for an argument  A is defined. We say that  F is defined at  A if a  F is a function restricted to the member  A of its domain. (Contributed by Alexander van der Vekens, 25-May-2017.)
Assertion
Ref Expression
df-dfat  |-  ( F defAt 
A  <->  ( A  e. 
dom  F  /\  Fun  ( F  |`  { A }
) ) )

Detailed syntax breakdown of Definition df-dfat
StepHypRef Expression
1 cA . . 3  class  A
2 cF . . 3  class  F
31, 2wdfat 27971 . 2  wff  F defAt  A
42cdm 4689 . . . 4  class  dom  F
51, 4wcel 1684 . . 3  wff  A  e. 
dom  F
61csn 3640 . . . . 5  class  { A }
72, 6cres 4691 . . . 4  class  ( F  |`  { A } )
87wfun 5249 . . 3  wff  Fun  ( F  |`  { A }
)
95, 8wa 358 . 2  wff  ( A  e.  dom  F  /\  Fun  ( F  |`  { A } ) )
103, 9wb 176 1  wff  ( F defAt 
A  <->  ( A  e. 
dom  F  /\  Fun  ( F  |`  { A }
) ) )
Colors of variables: wff set class
This definition is referenced by:  dfateq12d  27992  nfdfat  27993  dfdfat2  27994  ndmafv  28003  nfunsnafv  28005  afvpcfv0  28009  afvfvn0fveq  28013  afv0nbfvbi  28014  fnbrafvb  28016  afvelrn  28030  afvres  28034  tz6.12-afv  28035  dmfcoafv  28036  afvco2  28037  aovmpt4g  28061
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