Theorem hlex 31434

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 6887	1 ⊢ 𝑋 ∈ V

This proof depends on syntax axioms:   = wceq 1570   ∈ wcel 2145  Vcvv 3450  ‘cfv 6527  BaseSetcba 31122

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2147  ax-9 2155  ax-ext 2732  ax-nul 5259

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2739  df-cleq 2752  df-clel 2835  df-ne 2956  df-v 3452  df-dif 3901  df-un 3903  df-ss 3915  df-nul 4279  df-sn 4584  df-pr 4586  df-uni 4867  df-iota 6483  df-fv 6535

This theorem is used by:  h2hcau  31515  h2hlm  31516  axhilex-zf  31517