Theorem vn0 3883

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 3176	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 3882	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2780  Vcvv 3173  ∅c0 3874

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590

This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-ne 2782  df-v 3175  df-dif 3543  df-nul 3875

This theorem is referenced by:  uniintsn  4449  relrelss  5576  imasaddfnlem  16011  imasvscafn  16020  cmpfi  21021  fclscmp  21644  compne  37665