Theorem vn0m 3426

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 2733	. 2 ⊢ 𝑥 ∈ V
2		19.8a 1583	. 2 ⊢ (𝑥 ∈ V → ∃𝑥 𝑥 ∈ V)
3	1, 2	ax-mp 5	1 ⊢ ∃𝑥 𝑥 ∈ V

Syntax hints:  ∃wex 1485   ∈ wcel 2141  Vcvv 2730

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 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-v 2732

This theorem is referenced by:  relrelss  5137