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Theorem bnrel 22219
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 22218 . . 3  |-  ( x  e.  CBan  ->  x  e.  NrmCVec )
21ssriv 3297 . 2  |-  CBan  C_  NrmCVec
3 nvrel 21931 . 2  |-  Rel  NrmCVec
4 relss 4905 . 2  |-  ( CBan  C_  NrmCVec  ->  ( Rel  NrmCVec  ->  Rel  CBan ) )
52, 3, 4mp2 9 1  |-  Rel  CBan
Colors of variables: wff set class
Syntax hints:    C_ wss 3265   Rel wrel 4825   NrmCVeccnv 21913   CBanccbn 22214
This theorem is referenced by:  hlrel  22242
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1661  ax-8 1682  ax-14 1721  ax-6 1736  ax-7 1741  ax-11 1753  ax-12 1939  ax-ext 2370  ax-sep 4273  ax-nul 4281  ax-pr 4346
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2376  df-cleq 2382  df-clel 2385  df-nfc 2514  df-ne 2554  df-rex 2657  df-rab 2660  df-v 2903  df-dif 3268  df-un 3270  df-in 3272  df-ss 3279  df-nul 3574  df-if 3685  df-sn 3765  df-pr 3766  df-op 3768  df-uni 3960  df-br 4156  df-opab 4210  df-xp 4826  df-rel 4827  df-iota 5360  df-fv 5404  df-oprab 6026  df-nv 21921  df-cbn 22215
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