Theorem vnex 2710

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 2708	. 2 |- -. V e. V
2		isset 1810	. 2 |- (V e. V <-> E.x x = V)
3	1, 2	mtbi 191	1 |- -. E.x x = V

Syntax hints:  -. wn 2   = wceq 954   e. wcel 956  E.wex 978  Vcvv 1807

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 961  ax-8 962  ax-12 966  ax-13 967  ax-14 968  ax-17 969  ax-4 971  ax-5o 973  ax-6o 976  ax-9o 1121  ax-ext 1457  ax-sep 2698

This theorem depends on definitions:  df-bi 147  df-an 225  df-ex 979  df-sb 1170  df-clab 1462  df-cleq 1467  df-clel 1470  df-v 1808

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