Theorem hlex 31159

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 6885	1 ⊢ 𝑋 ∈ V

Syntax hints:   = wceq 1563   ∈ wcel 2145  Vcvv 3457  ‘cfv 6525  BaseSetcba 30847

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031  ax-8 2147  ax-9 2155  ax-ext 2737  ax-nul 5261

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-tru 1566  df-fal 1576  df-ex 1803  df-sb 2094  df-clab 2744  df-cleq 2757  df-clel 2840  df-ne 2961  df-v 3459  df-dif 3910  df-un 3912  df-ss 3924  df-nul 4289  df-sn 4586  df-pr 4588  df-uni 4869  df-iota 6481  df-fv 6533

This theorem is referenced by:  h2hcau  31240  h2hlm  31241  axhilex-zf  31242