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Theorem hlrel 28673
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 28671 . . 3 (𝑥 ∈ CHilOLD𝑥 ∈ CBan)
21ssriv 3919 . 2 CHilOLD ⊆ CBan
3 bnrel 28650 . 2 Rel CBan
4 relss 5620 . 2 (CHilOLD ⊆ CBan → (Rel CBan → Rel CHilOLD))
52, 3, 4mp2 9 1 Rel CHilOLD
Colors of variables: wff setvar class
Syntax hints:  wss 3881  Rel wrel 5524  CBanccbn 28645  CHilOLDchlo 28668
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-10 2142  ax-11 2158  ax-12 2175  ax-ext 2770  ax-sep 5167  ax-nul 5174  ax-pr 5295
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-nfc 2938  df-rab 3115  df-v 3443  df-dif 3884  df-un 3886  df-in 3888  df-ss 3898  df-nul 4244  df-if 4426  df-sn 4526  df-pr 4528  df-op 4532  df-uni 4801  df-br 5031  df-opab 5093  df-xp 5525  df-rel 5526  df-iota 6283  df-fv 6332  df-oprab 7139  df-nv 28375  df-cbn 28646  df-hlo 28669
This theorem is referenced by: (None)
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