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Theorem relprcnfsupp 7721
Description: A proper class is never finitely supported. (Contributed by AV, 7-Jun-2019.)
Assertion
Ref Expression
relprcnfsupp  |-  ( -.  A  e.  _V  ->  -.  A finSupp  Z )

Proof of Theorem relprcnfsupp
StepHypRef Expression
1 relfsupp 7720 . . 3  |-  Rel finSupp
21brrelexi 4974 . 2  |-  ( A finSupp  Z  ->  A  e.  _V )
32con3i 135 1  |-  ( -.  A  e.  _V  ->  -.  A finSupp  Z )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    e. wcel 1758   _Vcvv 3065   class class class wbr 4387   finSupp cfsupp 7718
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-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1952  ax-ext 2430  ax-sep 4508  ax-nul 4516  ax-pr 4626
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 967  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2599  df-ne 2644  df-ral 2798  df-rex 2799  df-rab 2802  df-v 3067  df-dif 3426  df-un 3428  df-in 3430  df-ss 3437  df-nul 3733  df-if 3887  df-sn 3973  df-pr 3975  df-op 3979  df-br 4388  df-opab 4446  df-xp 4941  df-rel 4942  df-fsupp 7719
This theorem is referenced by:  fsuppres  7743
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