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Theorem hlex 26956
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 5996 . 2 (BaseSet‘𝑈) ∈ V
31, 2eqeltri 2588 1 𝑋 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1474  wcel 1938  Vcvv 3077  cfv 5689  BaseSetcba 26611
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1700  ax-4 1713  ax-5 1793  ax-6 1838  ax-7 1885  ax-10 1966  ax-11 1971  ax-12 1983  ax-13 2137  ax-ext 2494  ax-nul 4616
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1699  df-sb 1831  df-eu 2366  df-clab 2501  df-cleq 2507  df-clel 2510  df-nfc 2644  df-ral 2805  df-rex 2806  df-v 3079  df-sbc 3307  df-dif 3447  df-un 3449  df-in 3451  df-ss 3458  df-nul 3778  df-sn 4029  df-pr 4031  df-uni 4271  df-iota 5653  df-fv 5697
This theorem is referenced by:  htthlem  26976  h2hcau  27038  h2hlm  27039  axhilex-zf  27040
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