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Theorem hlex 21477
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 5539 . 2  |-  ( BaseSet `  U )  e.  _V
31, 2eqeltri 2353 1  |-  X  e. 
_V
Colors of variables: wff set class
Syntax hints:    = wceq 1623    e. wcel 1684   _Vcvv 2788   ` cfv 5255   BaseSetcba 21142
This theorem is referenced by:  htthlem  21497  h2hcau  21559  h2hlm  21560  axhilex-zf  21561
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-nul 4149
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-eu 2147  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-ral 2548  df-rex 2549  df-v 2790  df-sbc 2992  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-sn 3646  df-pr 3647  df-uni 3828  df-iota 5219  df-fv 5263
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