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Theorem bnrel 30614
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 30613 . . 3 (𝑥 ∈ CBan → 𝑥 ∈ NrmCVec)
21ssriv 3979 . 2 CBan ⊆ NrmCVec
3 nvrel 30349 . 2 Rel NrmCVec
4 relss 5772 . 2 (CBan ⊆ NrmCVec → (Rel NrmCVec → Rel CBan))
52, 3, 4mp2 9 1 Rel CBan
Colors of variables: wff setvar class
Syntax hints:  wss 3941  Rel wrel 5672  NrmCVeccnv 30331  CBanccbn 30609
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-11 2146  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pr 5418
This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-rab 3425  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-if 4522  df-sn 4622  df-pr 4624  df-op 4628  df-uni 4901  df-br 5140  df-opab 5202  df-xp 5673  df-rel 5674  df-iota 6486  df-fv 6542  df-oprab 7406  df-nv 30339  df-cbn 30610
This theorem is referenced by:  hlrel  30637
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