Theorem vnex 2712

Description: The universal class does not exist.

Assertion

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

Proof of Theorem vnex

Step	Hyp	Ref	Expression
1		nvelv 2710	. 2 |- -. V e. V
2		isset 1812	. 2 |- (V e. V <-> E.x x = V)
3	1, 2	mtbi 191	1 |- -. E.x x = V

Syntax hints:  -. wn 2   = wceq 955   e. wcel 957  E.wex 979  Vcvv 1809

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 962  ax-8 963  ax-12 967  ax-13 968  ax-14 969  ax-17 970  ax-4 972  ax-5o 974  ax-6o 977  ax-9o 1122  ax-ext 1459  ax-sep 2700

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 980  df-sb 1172  df-clab 1464  df-cleq 1469  df-clel 1472  df-v 1810

Copyright terms: Public domain