Theorem vprcOLD 5276

Description: Obsolete proof of vprc 5275, 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 5272	. 2 ⊢ ¬ ∃𝑥 𝑥 = V
2		isset 3471	. 2 ⊢ (V ∈ V ↔ ∃𝑥 𝑥 = V)
3	1, 2	mtbir 326	1 ⊢ ¬ V ∈ V

Syntax hints:  ¬ wn 3   = wceq 1563  ∃wex 1802   ∈ wcel 2145  Vcvv 3457

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737  ax-sep 5251

This theorem depends on definitions:  df-bi 210  df-an 401  df-tru 1566  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-v 3459

This theorem is referenced by: (None)