Theorem vn0m 3458

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 2763	. 2 |- x e. _V
2		19.8a 1601	. 2 |- ( x e. _V -> E. x x e. _V )
3	1, 2	ax-mp 5	1 |- E. x x e. _V

Syntax hints:   E.wex 1503   e. wcel 2164   _Vcvv 2760

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-v 2762

This theorem is referenced by:  relrelss  5192  imasaddfnlemg  12897