Theorem hlex 30623

Description: The base set of a Hilbert space is a set. (Contributed by NM, 7-Sep-2007.) (New usage is discouraged.)

Hypothesis

Ref	Expression
hlex.1	⊢ 𝑋 = (BaseSet‘𝑈)

Assertion

Ref	Expression
hlex	⊢ 𝑋 ∈ V

Proof of Theorem hlex

Step	Hyp	Ref	Expression
1		hlex.1	. 2 ⊢ 𝑋 = (BaseSet‘𝑈)
2	1	fvexi 6896	1 ⊢ 𝑋 ∈ V

Syntax hints:   = wceq 1533   ∈ wcel 2098  Vcvv 3466  ‘cfv 6534  BaseSetcba 30311

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-nul 5297

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-ne 2933  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-sn 4622  df-pr 4624  df-uni 4901  df-iota 6486  df-fv 6542

This theorem is referenced by:  h2hcau  30704  h2hlm  30705  axhilex-zf  30706