Theorem hlex 31040

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 6870	1 ⊢ 𝑋 ∈ V

Syntax hints:   = wceq 1554   ∈ wcel 2136  Vcvv 3448  ‘cfv 6510  BaseSetcba 30728

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1809  ax-4 1823  ax-5 1924  ax-6 1981  ax-7 2022  ax-8 2138  ax-9 2146  ax-ext 2728  ax-nul 5250

This theorem depends on definitions:  df-bi 209  df-an 399  df-or 857  df-tru 1557  df-fal 1567  df-ex 1794  df-sb 2085  df-clab 2735  df-cleq 2748  df-clel 2831  df-ne 2952  df-v 3450  df-dif 3902  df-un 3904  df-ss 3916  df-nul 4281  df-sn 4577  df-pr 4579  df-uni 4860  df-iota 6466  df-fv 6518

This theorem is referenced by:  h2hcau  31121  h2hlm  31122  axhilex-zf  31123