MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  hlex Structured version   Visualization version   GIF version

Theorem hlex 30918
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 6919 1 𝑋 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  wcel 2107  Vcvv 3479  cfv 6560  BaseSetcba 30606
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707  ax-nul 5305
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-ne 2940  df-v 3481  df-dif 3953  df-un 3955  df-ss 3967  df-nul 4333  df-sn 4626  df-pr 4628  df-uni 4907  df-iota 6513  df-fv 6568
This theorem is referenced by:  h2hcau  30999  h2hlm  31000  axhilex-zf  31001
  Copyright terms: Public domain W3C validator