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Theorem hlrel 30909
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 30907 . . 3 (𝑥 ∈ CHilOLD𝑥 ∈ CBan)
21ssriv 3987 . 2 CHilOLD ⊆ CBan
3 bnrel 30886 . 2 Rel CBan
4 relss 5791 . 2 (CHilOLD ⊆ CBan → (Rel CBan → Rel CHilOLD))
52, 3, 4mp2 9 1 Rel CHilOLD
Colors of variables: wff setvar class
Syntax hints:  wss 3951  Rel wrel 5690  CBanccbn 30881  CHilOLDchlo 30904
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-11 2157  ax-ext 2708  ax-sep 5296  ax-nul 5306  ax-pr 5432
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-in 3958  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-opab 5206  df-xp 5691  df-rel 5692  df-iota 6514  df-fv 6569  df-oprab 7435  df-nv 30611  df-cbn 30882  df-hlo 30905
This theorem is referenced by: (None)
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