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Theorem hlex 26012
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 5858 . 2  |-  ( BaseSet `  U )  e.  _V
31, 2eqeltri 2538 1  |-  X  e. 
_V
Colors of variables: wff setvar class
Syntax hints:    = wceq 1398    e. wcel 1823   _Vcvv 3106   ` cfv 5570   BaseSetcba 25677
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432  ax-nul 4568
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-eu 2288  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2651  df-ral 2809  df-rex 2810  df-v 3108  df-sbc 3325  df-dif 3464  df-un 3466  df-in 3468  df-ss 3475  df-nul 3784  df-sn 4017  df-pr 4019  df-uni 4236  df-iota 5534  df-fv 5578
This theorem is referenced by:  htthlem  26032  h2hcau  26094  h2hlm  26095  axhilex-zf  26096
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