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Theorem relprcnfsupp 9109
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 9108 . . 3 Rel finSupp
21brrelex1i 5644 . 2 (𝐴 finSupp 𝑍𝐴 ∈ V)
32con3i 154 1 𝐴 ∈ V → ¬ 𝐴 finSupp 𝑍)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wcel 2110  Vcvv 3431   class class class wbr 5079   finSupp cfsupp 9106
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1975  ax-7 2015  ax-8 2112  ax-9 2120  ax-ext 2711  ax-sep 5227  ax-nul 5234  ax-pr 5356
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-3an 1088  df-tru 1545  df-fal 1555  df-ex 1787  df-sb 2072  df-clab 2718  df-cleq 2732  df-clel 2818  df-ral 3071  df-rex 3072  df-rab 3075  df-v 3433  df-dif 3895  df-un 3897  df-in 3899  df-ss 3909  df-nul 4263  df-if 4466  df-sn 4568  df-pr 4570  df-op 4574  df-br 5080  df-opab 5142  df-xp 5596  df-rel 5597  df-fsupp 9107
This theorem is referenced by:  fsuppres  9131
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