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Theorem afvprc 27678
Description: A function's value at a proper class is the universe, compare with fvprc 5663. (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 2908 . . 3  |-  ( A  e.  dom  F  ->  A  e.  _V )
21con3i 129 . 2  |-  ( -.  A  e.  _V  ->  -.  A  e.  dom  F
)
3 ndmafv 27674 . 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 1649    e. wcel 1717   _Vcvv 2900   dom cdm 4819  '''cafv 27641
This theorem is referenced by:  afvvv  27679
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2369
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2375  df-cleq 2381  df-clel 2384  df-nfc 2513  df-rab 2659  df-v 2902  df-un 3269  df-if 3684  df-fv 5403  df-dfat 27643  df-afv 27644
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