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Theorem bnrel 30887
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 30886 . . 3 (𝑥 ∈ CBan → 𝑥 ∈ NrmCVec)
21ssriv 3986 . 2 CBan ⊆ NrmCVec
3 nvrel 30622 . 2 Rel NrmCVec
4 relss 5790 . 2 (CBan ⊆ NrmCVec → (Rel NrmCVec → Rel CBan))
52, 3, 4mp2 9 1 Rel CBan
Colors of variables: wff setvar class
Syntax hints:  wss 3950  Rel wrel 5689  NrmCVeccnv 30604  CBanccbn 30882
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-11 2156  ax-ext 2707  ax-sep 5295  ax-nul 5305  ax-pr 5431
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-rab 3436  df-v 3481  df-dif 3953  df-un 3955  df-ss 3967  df-nul 4333  df-if 4525  df-sn 4626  df-pr 4628  df-op 4632  df-uni 4907  df-br 5143  df-opab 5205  df-xp 5690  df-rel 5691  df-iota 6513  df-fv 6568  df-oprab 7436  df-nv 30612  df-cbn 30883
This theorem is referenced by:  hlrel  30910
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