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Theorem hlex 21437
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 5472 . 2  |-  ( BaseSet `  U )  e.  _V
31, 2eqeltri 2328 1  |-  X  e. 
_V
Colors of variables: wff set class
Syntax hints:    = wceq 1619    e. wcel 1621   _Vcvv 2763   ` cfv 4673   BaseSetcba 21102
This theorem is referenced by:  htthlem  21457  h2hcau  21519  h2hlm  21520  axhilex-zf  21521
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-13 1625  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2239  ax-sep 4115  ax-nul 4123  ax-pr 4186  ax-un 4484
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2122  df-mo 2123  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-ne 2423  df-rex 2524  df-v 2765  df-dif 3130  df-un 3132  df-in 3134  df-ss 3141  df-nul 3431  df-sn 3620  df-pr 3621  df-uni 3802  df-fv 4689
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