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Theorem hlrel 21394
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 21392 . . 3  |-  ( x  e.  CHil OLD  ->  x  e. 
CBan )
21ssriv 3126 . 2  |-  CHil OLD  C_ 
CBan
3 bnrel 21371 . 2  |-  Rel  CBan
4 relss 4728 . 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 3094   Rel wrel 4631   CBanccbn 21366   CHil OLDchlo 21389
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 1927  ax-ext 2237  ax-sep 4081  ax-nul 4089  ax-pr 4152
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 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-ne 2421  df-rex 2521  df-rab 2523  df-v 2742  df-dif 3097  df-un 3099  df-in 3101  df-ss 3108  df-nul 3398  df-if 3507  df-sn 3587  df-pr 3588  df-op 3590  df-uni 3769  df-br 3964  df-opab 4018  df-xp 4640  df-rel 4641  df-cnv 4642  df-dm 4644  df-rn 4645  df-res 4646  df-ima 4647  df-fv 4654  df-oprab 5761  df-nv 21073  df-cbn 21367  df-hlo 21390
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