Theorem vprcOLD 5256

Description: Obsolete proof of vprc 5255, 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 5252	. 2 ⊢ ¬ ∃𝑥 𝑥 = V
2		isset 3443	. 2 ⊢ (V ∈ V ↔ ∃𝑥 𝑥 = V)
3	1, 2	mtbir 323	1 ⊢ ¬ V ∈ V

Syntax hints:  ¬ wn 3   = wceq 1542  ∃wex 1781   ∈ wcel 2114  Vcvv 3429

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2708  ax-sep 5231

This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1545  df-ex 1782  df-sb 2069  df-clab 2715  df-cleq 2728  df-clel 2811  df-v 3431

This theorem is referenced by: (None)