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Theorem hlrel 22345
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 22343 . . 3  |-  ( x  e.  CHil OLD  ->  x  e. 
CBan )
21ssriv 3312 . 2  |-  CHil OLD  C_ 
CBan
3 bnrel 22322 . 2  |-  Rel  CBan
4 relss 4922 . 2  |-  ( CHil
OLD  C_  CBan  ->  ( Rel 
CBan  ->  Rel  CHil OLD )
)
52, 3, 4mp2 9 1  |-  Rel  CHil OLD
Colors of variables: wff set class
Syntax hints:    C_ wss 3280   Rel wrel 4842   CBanccbn 22317   CHil OLDchlo 22340
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-14 1725  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385  ax-sep 4290  ax-nul 4298  ax-pr 4363
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-ne 2569  df-rex 2672  df-rab 2675  df-v 2918  df-dif 3283  df-un 3285  df-in 3287  df-ss 3294  df-nul 3589  df-if 3700  df-sn 3780  df-pr 3781  df-op 3783  df-uni 3976  df-br 4173  df-opab 4227  df-xp 4843  df-rel 4844  df-iota 5377  df-fv 5421  df-oprab 6044  df-nv 22024  df-cbn 22318  df-hlo 22341
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