Theorem vn0 3924

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 3203	. 2 |- x e. _V
2	1	ne0ii 3923	1 |- _V =/= (/)

Syntax hints:   =/= wne 2794   _Vcvv 3200   (/)c0 3915

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-ne 2795  df-v 3202  df-dif 3577  df-nul 3916

This theorem is referenced by:  uniintsn  4514  relrelss  5659  imasaddfnlem  16188  imasvscafn  16197  cmpfi  21211  fclscmp  21834  compne  38643  compneOLD  38644