Theorem vn0 4156

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 3417	. 2 ⊢ 𝑥 ∈ V
2	1	ne0ii 4155	1 ⊢ V ≠ ∅

Syntax hints:   ≠ wne 2999  Vcvv 3414  ∅c0 4146

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1894  ax-4 1908  ax-5 2009  ax-6 2075  ax-7 2112  ax-9 2173  ax-10 2192  ax-11 2207  ax-12 2220  ax-ext 2803

This theorem depends on definitions:  df-bi 199  df-an 387  df-or 879  df-tru 1660  df-ex 1879  df-nf 1883  df-sb 2068  df-clab 2812  df-cleq 2818  df-clel 2821  df-nfc 2958  df-ne 3000  df-v 3416  df-dif 3801  df-nul 4147

This theorem is referenced by:  uniintsn  4736  relrelss  5904  imasaddfnlem  16548  imasvscafn  16557  cmpfi  21589  fclscmp  22211  compne  39481  compneOLD  39482