Theorem vn0 4306

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 3499	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4305	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 3018  Vcvv 3496  ∅c0 4293

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 2795

This theorem depends on definitions:  df-bi 209  df-an 399  df-ex 1781  df-sb 2070  df-clab 2802  df-cleq 2816  df-clel 2895  df-ne 3019  df-v 3498  df-dif 3941  df-nul 4294

This theorem is referenced by:  uniintsn  4915  relrelss  6126  imasaddfnlem  16803  imasvscafn  16812  cmpfi  22018  fclscmp  22640  compne  40780