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Theorem hlrel 21469
Description: The class of all complex Hilbert spaces is a relation. (Contributed by NM, 17-Mar-2007.) (New usage is discouraged.)
Assertion
Ref Expression
hlrel  |-  Rel  CHil OLD

Proof of Theorem hlrel
StepHypRef Expression
1 hlobn 21467 . . 3  |-  ( x  e.  CHil OLD  ->  x  e. 
CBan )
21ssriv 3184 . 2  |-  CHil OLD  C_ 
CBan
3 bnrel 21446 . 2  |-  Rel  CBan
4 relss 4775 . 2  |-  ( CHil
OLD  C_  CBan  ->  ( Rel 
CBan  ->  Rel  CHil OLD )
)
52, 3, 4mp2 17 1  |-  Rel  CHil OLD
Colors of variables: wff set class
Syntax hints:    C_ wss 3152   Rel wrel 4694   CBanccbn 21441   CHil OLDchlo 21464
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-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rex 2549  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-uni 3828  df-br 4024  df-opab 4078  df-xp 4695  df-rel 4696  df-iota 5219  df-fv 5263  df-oprab 5862  df-nv 21148  df-cbn 21442  df-hlo 21465
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