Theorem vprcOLD 5270

Description: Obsolete proof of vprc 5269, 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 5266	. 2 ⊢ ¬ ∃𝑥 𝑥 = V
2		isset 3467	. 2 ⊢ (V ∈ V ↔ ∃𝑥 𝑥 = V)
3	1, 2	mtbir 325	1 ⊢ ¬ V ∈ V

Syntax hints:  ¬ wn 3   = wceq 1559  ∃wex 1798   ∈ wcel 2141  Vcvv 3453

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027  ax-8 2143  ax-9 2151  ax-ext 2733  ax-sep 5245

This theorem depends on definitions:  df-bi 209  df-an 400  df-tru 1562  df-ex 1799  df-sb 2090  df-clab 2740  df-cleq 2753  df-clel 2836  df-v 3455

This theorem is referenced by: (None)