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Theorem relprcnfsupp 8833
Description: A proper class is never finitely supported. (Contributed by AV, 7-Jun-2019.)
Assertion
Ref Expression
relprcnfsupp 𝐴 ∈ V → ¬ 𝐴 finSupp 𝑍)

Proof of Theorem relprcnfsupp
StepHypRef Expression
1 relfsupp 8832 . . 3 Rel finSupp
21brrelex1i 5595 . 2 (𝐴 finSupp 𝑍𝐴 ∈ V)
32con3i 157 1 𝐴 ∈ V → ¬ 𝐴 finSupp 𝑍)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2115  Vcvv 3480   class class class wbr 5052   finSupp cfsupp 8830
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5189  ax-nul 5196  ax-pr 5317
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-rex 3139  df-v 3482  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-if 4451  df-sn 4551  df-pr 4553  df-op 4557  df-br 5053  df-opab 5115  df-xp 5548  df-rel 5549  df-fsupp 8831
This theorem is referenced by:  fsuppres  8855
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