Theorem vn0m 3420

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 2729	. 2 ⊢ 𝑥 ∈ V
2		19.8a 1578	. 2 ⊢ (𝑥 ∈ V → ∃𝑥 𝑥 ∈ V)
3	1, 2	ax-mp 5	1 ⊢ ∃𝑥 𝑥 ∈ V

Syntax hints:  ∃wex 1480   ∈ wcel 2136  Vcvv 2726

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1435  ax-gen 1437  ax-ie1 1481  ax-ie2 1482  ax-8 1492  ax-4 1498  ax-17 1514  ax-i9 1518  ax-ial 1522  ax-ext 2147

This theorem depends on definitions:  df-bi 116  df-sb 1751  df-clab 2152  df-cleq 2158  df-clel 2161  df-v 2728

This theorem is referenced by:  relrelss  5130