Theorem vn0m 3454

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

Assertion

Ref	Expression
vn0m	⊢ ∃𝑥 𝑥 ∈ V

Proof of Theorem vn0m

Step	Hyp	Ref	Expression
1		vex 2759	. 2 ⊢ 𝑥 ∈ V
2		19.8a 1601	. 2 ⊢ (𝑥 ∈ V → ∃𝑥 𝑥 ∈ V)
3	1, 2	ax-mp 5	1 ⊢ ∃𝑥 𝑥 ∈ V

Syntax hints:  ∃wex 1503   ∈ wcel 2160  Vcvv 2756

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 2171

This theorem depends on definitions:  df-bi 117  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-v 2758

This theorem is referenced by:  relrelss  5180  imasaddfnlemg  12871