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Theorem hlrel 30919
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 30917 . . 3 (𝑥 ∈ CHilOLD𝑥 ∈ CBan)
21ssriv 3999 . 2 CHilOLD ⊆ CBan
3 bnrel 30896 . 2 Rel CBan
4 relss 5794 . 2 (CHilOLD ⊆ CBan → (Rel CBan → Rel CHilOLD))
52, 3, 4mp2 9 1 Rel CHilOLD
Colors of variables: wff setvar class
Syntax hints:  wss 3963  Rel wrel 5694  CBanccbn 30891  CHilOLDchlo 30914
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-11 2155  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-in 3970  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-opab 5211  df-xp 5695  df-rel 5696  df-iota 6516  df-fv 6571  df-oprab 7435  df-nv 30621  df-cbn 30892  df-hlo 30915
This theorem is referenced by: (None)
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