Theorem relprcnfsupp 9337

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 9336	. . 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 2145  Vcvv 3450   class class class wbr 5103   finSupp cfsupp 9334

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732  ax-sep 5251  ax-pr 5398

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-ral 3077  df-rex 3087  df-rab 3413  df-v 3452  df-dif 3902  df-un 3904  df-in 3906  df-ss 3916  df-nul 4280  df-if 4483  df-sn 4585  df-pr 4587  df-op 4591  df-br 5104  df-opab 5168  df-xp 5661  df-rel 5662  df-fsupp 9335

This theorem is used by:  fsuppres  9366