Theorem vn0 4304

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 3497	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4303	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 3016  Vcvv 3494  ∅c0 4291

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2116  ax-9 2124  ax-ext 2793

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1781  df-sb 2070  df-clab 2800  df-cleq 2814  df-clel 2893  df-ne 3017  df-v 3496  df-dif 3939  df-nul 4292

This theorem is referenced by:  uniintsn  4913  relrelss  6124  imasaddfnlem  16801  imasvscafn  16810  cmpfi  22016  fclscmp  22638  compne  40793