Metamath Proof Explorer

Theorem vnex

Description: The universal class does not exist as a set. (Contributed by NM, 4-Jul-2005) (Proof shortened by BJ, 25-Apr-2026)

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

Proof

Step Hyp Ref Expression
1 vneqv 
 |-  -. x = _V
2 1 nex 
 |-  -. E. x x = _V