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Theorem relprcnfsupp 7839
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 7838 . . 3  |-  Rel finSupp
21brrelexi 4837 . 2  |-  ( A finSupp  Z  ->  A  e.  _V )
32con3i 140 1  |-  ( -.  A  e.  _V  ->  -.  A finSupp  Z )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    e. wcel 1872   _Vcvv 3022   class class class wbr 4366   finSupp cfsupp 7836
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-9 1876  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408  ax-sep 4489  ax-nul 4498  ax-pr 4603
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-ne 2601  df-ral 2719  df-rex 2720  df-rab 2723  df-v 3024  df-dif 3382  df-un 3384  df-in 3386  df-ss 3393  df-nul 3705  df-if 3855  df-sn 3942  df-pr 3944  df-op 3948  df-br 4367  df-opab 4426  df-xp 4802  df-rel 4803  df-fsupp 7837
This theorem is referenced by:  fsuppres  7861
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