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Theorem hlrel 26527
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  CHilOLD

Proof of Theorem hlrel
StepHypRef Expression
1 hlobn 26525 . . 3  |-  ( x  e.  CHilOLD  ->  x  e.  CBan )
21ssriv 3468 . 2  |-  CHilOLD  C_ 
CBan
3 bnrel 26494 . 2  |-  Rel  CBan
4 relss 4937 . 2  |-  ( CHilOLD  C_  CBan  ->  ( Rel 
CBan  ->  Rel  CHilOLD )
)
52, 3, 4mp2 9 1  |-  Rel  CHilOLD
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3436   Rel wrel 4854   CBanccbn 26489   CHilOLDchlo 26522
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-9 1872  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400  ax-sep 4543  ax-nul 4551  ax-pr 4656
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-nfc 2572  df-ne 2620  df-rex 2781  df-rab 2784  df-v 3083  df-dif 3439  df-un 3441  df-in 3443  df-ss 3450  df-nul 3762  df-if 3910  df-sn 3997  df-pr 3999  df-op 4003  df-uni 4217  df-br 4421  df-opab 4480  df-xp 4855  df-rel 4856  df-iota 5561  df-fv 5605  df-oprab 6305  df-nv 26196  df-cbn 26490  df-hlo 26523
This theorem is referenced by: (None)
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