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Theorem afvprc 27975
Description: A function's value at a proper class is the universe, compare with fvprc 5714. (Contributed by Alexander van der Vekens, 25-May-2017.)
Assertion
Ref Expression
afvprc  |-  ( -.  A  e.  _V  ->  ( F''' A )  =  _V )

Proof of Theorem afvprc
StepHypRef Expression
1 elex 2956 . . 3  |-  ( A  e.  dom  F  ->  A  e.  _V )
21con3i 129 . 2  |-  ( -.  A  e.  _V  ->  -.  A  e.  dom  F
)
3 ndmafv 27971 . 2  |-  ( -.  A  e.  dom  F  ->  ( F''' A )  =  _V )
42, 3syl 16 1  |-  ( -.  A  e.  _V  ->  ( F''' A )  =  _V )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1652    e. wcel 1725   _Vcvv 2948   dom cdm 4870  '''cafv 27939
This theorem is referenced by:  afvvv  27976
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-rab 2706  df-v 2950  df-un 3317  df-if 3732  df-fv 5454  df-dfat 27941  df-afv 27942
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