Theorem vn0 4254

Description: The universal class is not equal to the empty set. (Contributed by NM, 11-Sep-2008.)

Assertion

Ref	Expression
vn0	⊢ V ≠ ∅

Proof of Theorem vn0

Step	Hyp	Ref	Expression
1		vex 3444	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4253	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2987  Vcvv 3441  ∅c0 4243

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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770

This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-ne 2988  df-v 3443  df-dif 3884  df-nul 4244

This theorem is referenced by:  uniintsn  4875  relrelss  6092  imasaddfnlem  16793  imasvscafn  16802  cmpfi  22013  fclscmp  22635  zarcmplem  31234  compne  41145