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Theorem bnrel 27107
 Description: The class of all complex Banach spaces is a relation. (Contributed by NM, 17-Mar-2007.) (New usage is discouraged.)
Assertion
Ref Expression
bnrel Rel CBan

Proof of Theorem bnrel
StepHypRef Expression
1 bnnv 27106 . . 3 (𝑥 ∈ CBan → 𝑥 ∈ NrmCVec)
21ssriv 3572 . 2 CBan ⊆ NrmCVec
3 nvrel 26841 . 2 Rel NrmCVec
4 relss 5129 . 2 (CBan ⊆ NrmCVec → (Rel NrmCVec → Rel CBan))
52, 3, 4mp2 9 1 Rel CBan
 Colors of variables: wff setvar class Syntax hints:   ⊆ wss 3540  Rel wrel 5043  NrmCVeccnv 26823  CBanccbn 27102 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-3an 1033  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rex 2902  df-rab 2905  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-if 4037  df-sn 4126  df-pr 4128  df-op 4132  df-uni 4373  df-br 4584  df-opab 4644  df-xp 5044  df-rel 5045  df-iota 5768  df-fv 5812  df-oprab 6553  df-nv 26831  df-cbn 27103 This theorem is referenced by:  hlrel  27130
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