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Theorem hlex 28690
 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 6677 1 𝑋 ∈ V
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∈ wcel 2115  Vcvv 3480  ‘cfv 6345  BaseSetcba 28378 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-nul 5197 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-mo 2624  df-eu 2655  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-ral 3138  df-rex 3139  df-v 3482  df-sbc 3759  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-sn 4551  df-pr 4553  df-uni 4825  df-iota 6304  df-fv 6353 This theorem is referenced by:  h2hcau  28771  h2hlm  28772  axhilex-zf  28773
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