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Theorem bnrel 28295
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 28294 . . 3 (𝑥 ∈ CBan → 𝑥 ∈ NrmCVec)
21ssriv 3825 . 2 CBan ⊆ NrmCVec
3 nvrel 28029 . 2 Rel NrmCVec
4 relss 5454 . 2 (CBan ⊆ NrmCVec → (Rel NrmCVec → Rel CBan))
52, 3, 4mp2 9 1 Rel CBan
Colors of variables: wff setvar class
Syntax hints:  wss 3792  Rel wrel 5360  NrmCVeccnv 28011  CBanccbn 28290
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1839  ax-4 1853  ax-5 1953  ax-6 2021  ax-7 2055  ax-9 2116  ax-10 2135  ax-11 2150  ax-12 2163  ax-13 2334  ax-ext 2754  ax-sep 5017  ax-nul 5025  ax-pr 5138
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 837  df-3an 1073  df-tru 1605  df-ex 1824  df-nf 1828  df-sb 2012  df-clab 2764  df-cleq 2770  df-clel 2774  df-nfc 2921  df-rex 3096  df-rab 3099  df-v 3400  df-dif 3795  df-un 3797  df-in 3799  df-ss 3806  df-nul 4142  df-if 4308  df-sn 4399  df-pr 4401  df-op 4405  df-uni 4672  df-br 4887  df-opab 4949  df-xp 5361  df-rel 5362  df-iota 6099  df-fv 6143  df-oprab 6926  df-nv 28019  df-cbn 28291
This theorem is referenced by:  hlrel  28318
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