Theorem vnex 3890

Description: The universal class does not exist. (Contributed by NM, 4-Jul-2005.)

Assertion

Ref	Expression
vnex	|- -. E. x x = _V

Proof of Theorem vnex

Step	Hyp	Ref	Expression
1		vprc 3888	. 2 |- -. _V e. _V
2		isset 2561	. 2 |- ( _V e. _V <-> E. x x = _V )
3	1, 2	mtbi 595	1 |- -. E. x x = _V

Syntax hints:   -. wn 3   = wceq 1243   E.wex 1381   e. wcel 1393   _Vcvv 2557

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-4 1400  ax-13 1404  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-ext 2022  ax-sep 3875

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-fal 1249  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-v 2559

This theorem is referenced by: (None)