Theorem vn0m 3463

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 2766	. 2 ⊢ 𝑥 ∈ V
2		19.8a 1604	. 2 ⊢ (𝑥 ∈ V → ∃𝑥 𝑥 ∈ V)
3	1, 2	ax-mp 5	1 ⊢ ∃𝑥 𝑥 ∈ V

Syntax hints:  ∃wex 1506   ∈ wcel 2167  Vcvv 2763

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-v 2765

This theorem is referenced by:  relrelss  5197  imasaddfnlemg  13016