Theorem vprcOLD 5280

Description: Obsolete proof of vprc 5279, obsolete as of 1-May-2026. (Contributed by NM, 23-Aug-1993.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
vprcOLD	⊢ ¬ V ∈ V

Proof of Theorem vprcOLD

Step	Hyp	Ref	Expression
1		vnex 5275	. 2 ⊢ ¬ ∃𝑥 𝑥 = V
2		isset 3468	. 2 ⊢ (V ∈ V ↔ ∃𝑥 𝑥 = V)
3	1, 2	mtbir 326	1 ⊢ ¬ V ∈ V

This proof depends on syntax axioms:  ¬ wn 3   = wceq 1570  ∃wex 1812   ∈ wcel 2147  Vcvv 3454

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-sep 5253

This proof depends on definitions:  df-bi 210  df-an 402  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456

This theorem is used by: (None)