Theorem vn0m 3533

Description: The universal class is inhabited. (Contributed by Jim Kingdon, 17-Dec-2018.)

Assertion

Ref	Expression
vn0m	|- E. x x e. _V

Proof of Theorem vn0m

Step	Hyp	Ref	Expression
1		vex 2824	. 2 |- x e. _V
2		19.8a 1643	. 2 |- ( x e. _V -> E. x x e. _V )
3	1, 2	ax-mp 5	1 |- E. x x e. _V

This proof depends on syntax axioms:   E.wex 1545   e. wcel 2209   _Vcvv 2821

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-v 2823

This theorem is used by:  relrelss  5314  imasaddfnlemg  13635