Theorem hlex 30927

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 6921	1 ⊢ 𝑋 ∈ V

Syntax hints:   = wceq 1537   ∈ wcel 2106  Vcvv 3478  ‘cfv 6563  BaseSetcba 30615

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-nul 5312

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-ne 2939  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-sn 4632  df-pr 4634  df-uni 4913  df-iota 6516  df-fv 6571

This theorem is referenced by:  h2hcau  31008  h2hlm  31009  axhilex-zf  31010