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Theorem hlex 30702
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 = (BaseSetβ€˜π‘ˆ)
Assertion
Ref Expression
hlex 𝑋 ∈ V

Proof of Theorem hlex
StepHypRef Expression
1 hlex.1 . 2 𝑋 = (BaseSetβ€˜π‘ˆ)
21fvexi 6906 1 𝑋 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1534   ∈ wcel 2099  Vcvv 3470  β€˜cfv 6543  BaseSetcba 30390
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699  ax-nul 5301
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-ne 2937  df-v 3472  df-dif 3948  df-un 3950  df-in 3952  df-ss 3962  df-nul 4320  df-sn 4626  df-pr 4628  df-uni 4905  df-iota 6495  df-fv 6551
This theorem is referenced by:  h2hcau  30783  h2hlm  30784  axhilex-zf  30785
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