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Theorem afvprc 30199
Description: A function's value at a proper class is the universe, compare with fvprc 5794. (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 3087 . . 3  |-  ( A  e.  dom  F  ->  A  e.  _V )
21con3i 135 . 2  |-  ( -.  A  e.  _V  ->  -.  A  e.  dom  F
)
3 ndmafv 30195 . 2  |-  ( -.  A  e.  dom  F  ->  ( F''' A )  =  _V )
42, 3syl 16 1  |-  ( -.  A  e.  _V  ->  ( F''' A )  =  _V )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    = wceq 1370    e. wcel 1758   _Vcvv 3078   dom cdm 4949  '''cafv 30167
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rab 2808  df-v 3080  df-un 3442  df-if 3901  df-fv 5535  df-dfat 30169  df-afv 30170
This theorem is referenced by:  afvvv  30200
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