Theorem relprcnfsupp 9360

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

Step	Hyp	Ref	Expression
1		relfsupp 9359	. . 3 ⊢ Rel finSupp
2	1	brrelex1i 5722	. 2 ⊢ (𝐴 finSupp 𝑍 → 𝐴 ∈ V)
3	2	con3i 154	1 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 finSupp 𝑍)

Syntax hints:  ¬ wn 3   → wi 4   ∈ wcel 2098  Vcvv 3466   class class class wbr 5138   finSupp cfsupp 9357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-sep 5289  ax-nul 5296  ax-pr 5417

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ral 3054  df-rex 3063  df-rab 3425  df-v 3468  df-dif 3943  df-un 3945  df-in 3947  df-ss 3957  df-nul 4315  df-if 4521  df-sn 4621  df-pr 4623  df-op 4627  df-br 5139  df-opab 5201  df-xp 5672  df-rel 5673  df-fsupp 9358

This theorem is referenced by:  fsuppres  9384