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Theorem bnrel 26183
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 26182 . . 3  |-  ( x  e.  CBan  ->  x  e.  NrmCVec )
21ssriv 3445 . 2  |-  CBan  C_  NrmCVec
3 nvrel 25895 . 2  |-  Rel  NrmCVec
4 relss 4910 . 2  |-  ( CBan  C_  NrmCVec  ->  ( Rel  NrmCVec  ->  Rel  CBan ) )
52, 3, 4mp2 9 1  |-  Rel  CBan
Colors of variables: wff setvar class
Syntax hints:    C_ wss 3413   Rel wrel 4827   NrmCVeccnv 25877   CBanccbn 26178
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4516  ax-nul 4524  ax-pr 4629
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-rex 2759  df-rab 2762  df-v 3060  df-dif 3416  df-un 3418  df-in 3420  df-ss 3427  df-nul 3738  df-if 3885  df-sn 3972  df-pr 3974  df-op 3978  df-uni 4191  df-br 4395  df-opab 4453  df-xp 4828  df-rel 4829  df-iota 5532  df-fv 5576  df-oprab 6281  df-nv 25885  df-cbn 26179
This theorem is referenced by:  hlrel  26206
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