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Theorem hlex 21493
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 5555 . 2  |-  ( BaseSet `  U )  e.  _V
31, 2eqeltri 2366 1  |-  X  e. 
_V
Colors of variables: wff set class
Syntax hints:    = wceq 1632    e. wcel 1696   _Vcvv 2801   ` cfv 5271   BaseSetcba 21158
This theorem is referenced by:  htthlem  21513  h2hcau  21575  h2hlm  21576  axhilex-zf  21577
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-nul 4165
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-eu 2160  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-ral 2561  df-rex 2562  df-v 2803  df-sbc 3005  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-sn 3659  df-pr 3660  df-uni 3844  df-iota 5235  df-fv 5279
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