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Theorem hlex 27724
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)
2 fvex 6188 . 2 (BaseSet‘𝑈) ∈ V
31, 2eqeltri 2695 1 𝑋 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1481  wcel 1988  Vcvv 3195  cfv 5876  BaseSetcba 27411
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1720  ax-4 1735  ax-5 1837  ax-6 1886  ax-7 1933  ax-9 1997  ax-10 2017  ax-11 2032  ax-12 2045  ax-13 2244  ax-ext 2600  ax-nul 4780
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1484  df-ex 1703  df-nf 1708  df-sb 1879  df-eu 2472  df-clab 2607  df-cleq 2613  df-clel 2616  df-nfc 2751  df-ral 2914  df-rex 2915  df-v 3197  df-sbc 3430  df-dif 3570  df-un 3572  df-in 3574  df-ss 3581  df-nul 3908  df-sn 4169  df-pr 4171  df-uni 4428  df-iota 5839  df-fv 5884
This theorem is referenced by:  htthlem  27744  h2hcau  27806  h2hlm  27807  axhilex-zf  27808
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