Theorem vprcOLD 5285

Description: Obsolete proof of vprc 5284, 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 5281	. 2 ⊢ ¬ ∃𝑥 𝑥 = V
2		isset 3469	. 2 ⊢ (V ∈ V ↔ ∃𝑥 𝑥 = V)
3	1, 2	mtbir 326	1 ⊢ ¬ V ∈ V

Syntax hints:  ¬ wn 3   = wceq 1570  ∃wex 1809   ∈ wcel 2143  Vcvv 3455

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-sep 5258

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1573  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-v 3457

This theorem is referenced by: (None)