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Theorem hlex 29257
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
StepHypRef Expression
1 hlex.1 . 2 𝑋 = (BaseSet‘𝑈)
21fvexi 6790 1 𝑋 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  wcel 2106  Vcvv 3431  cfv 6435  BaseSetcba 28945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-10 2137  ax-11 2154  ax-12 2171  ax-ext 2709  ax-nul 5232
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-fal 1552  df-ex 1783  df-nf 1787  df-sb 2068  df-mo 2540  df-eu 2569  df-clab 2716  df-cleq 2730  df-clel 2816  df-ral 3069  df-rex 3070  df-v 3433  df-dif 3891  df-un 3893  df-in 3895  df-ss 3905  df-nul 4259  df-sn 4564  df-pr 4566  df-uni 4842  df-iota 6393  df-fv 6443
This theorem is referenced by:  h2hcau  29338  h2hlm  29339  axhilex-zf  29340
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