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Theorem hlex 22400
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  e. 
_V

Proof of Theorem hlex
StepHypRef Expression
1 hlex.1 . 2  |-  X  =  ( BaseSet `  U )
2 fvex 5742 . 2  |-  ( BaseSet `  U )  e.  _V
31, 2eqeltri 2506 1  |-  X  e. 
_V
Colors of variables: wff set class
Syntax hints:    = wceq 1652    e. wcel 1725   _Vcvv 2956   ` cfv 5454   BaseSetcba 22065
This theorem is referenced by:  htthlem  22420  h2hcau  22482  h2hlm  22483  axhilex-zf  22484
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-nul 4338
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2285  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-ral 2710  df-rex 2711  df-v 2958  df-sbc 3162  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-sn 3820  df-pr 3821  df-uni 4016  df-iota 5418  df-fv 5462
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