Theorem hlex 30889

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 6845	1 ⊢ 𝑋 ∈ V

Syntax hints:   = wceq 1541   ∈ wcel 2113  Vcvv 3438  ‘cfv 6489  BaseSetcba 30577

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2705  ax-nul 5248

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2712  df-cleq 2725  df-clel 2808  df-ne 2931  df-v 3440  df-dif 3902  df-un 3904  df-ss 3916  df-nul 4285  df-sn 4578  df-pr 4580  df-uni 4861  df-iota 6445  df-fv 6497

This theorem is referenced by:  h2hcau  30970  h2hlm  30971  axhilex-zf  30972