Theorem relprcnfsupp 9370

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 9369	. . 3 ⊢ Rel finSupp
2	1	brrelex1i 5711	. 2 ⊢ (𝐴 finSupp 𝑍 → 𝐴 ∈ V)
3	2	con3i 155	1 ⊢ (¬ 𝐴 ∈ V → ¬ 𝐴 finSupp 𝑍)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∈ wcel 2146  Vcvv 3454   class class class wbr 5106   finSupp cfsupp 9367

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1944  ax-6 2001  ax-7 2042  ax-8 2148  ax-9 2156  ax-ext 2735  ax-sep 5252  ax-pr 5395

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1572  df-fal 1582  df-ex 1812  df-sb 2101  df-clab 2742  df-cleq 2755  df-clel 2839  df-ral 3081  df-rex 3091  df-rab 3417  df-v 3456  df-ss 3901  df-dif 4050  df-in 4094  df-un 4154  df-nul 4282  df-if 4486  df-sn 4589  df-pr 4591  df-op 4839  df-br 5107  df-opab 5171  df-xp 5661  df-rel 5662  df-fsupp 9368

This theorem is used by:  fsuppres  9398