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Theorem hlrel 21299
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 21297 . . 3  |-  ( x  e.  CHil OLD  ->  x  e. 
CBan )
21ssriv 3105 . 2  |-  CHil OLD  C_ 
CBan
3 bnrel 21276 . 2  |-  Rel  CBan
4 relss 4682 . 2  |-  ( CHil
OLD  C_  CBan  ->  ( Rel 
CBan  ->  Rel  CHil OLD )
)
52, 3, 4mp2 19 1  |-  Rel  CHil OLD
Colors of variables: wff set class
Syntax hints:    C_ wss 3078   Rel wrel 4585   CBanccbn 21271   CHil OLDchlo 21294
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234  ax-sep 4038  ax-nul 4046  ax-pr 4108
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-rex 2514  df-rab 2516  df-v 2729  df-dif 3081  df-un 3083  df-in 3085  df-ss 3089  df-nul 3363  df-if 3471  df-sn 3550  df-pr 3551  df-op 3553  df-uni 3728  df-br 3921  df-opab 3975  df-xp 4594  df-rel 4595  df-cnv 4596  df-dm 4598  df-rn 4599  df-res 4600  df-ima 4601  df-fv 4608  df-oprab 5714  df-nv 20978  df-cbn 21272  df-hlo 21295
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