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Theorem hlex 29882
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 = (BaseSetβ€˜π‘ˆ)
Assertion
Ref Expression
hlex 𝑋 ∈ V

Proof of Theorem hlex
StepHypRef Expression
1 hlex.1 . 2 𝑋 = (BaseSetβ€˜π‘ˆ)
21fvexi 6857 1 𝑋 ∈ V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542   ∈ wcel 2107  Vcvv 3444  β€˜cfv 6497  BaseSetcba 29570
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 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704  ax-nul 5264
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-ne 2941  df-v 3446  df-dif 3914  df-un 3916  df-in 3918  df-ss 3928  df-nul 4284  df-sn 4588  df-pr 4590  df-uni 4867  df-iota 6449  df-fv 6505
This theorem is referenced by:  h2hcau  29963  h2hlm  29964  axhilex-zf  29965
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