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Theorem bnrel 21462
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 21461 . . 3  |-  ( x  e.  CBan  ->  x  e.  NrmCVec )
21ssriv 3197 . 2  |-  CBan  C_  NrmCVec
3 nvrel 21174 . 2  |-  Rel  NrmCVec
4 relss 4791 . 2  |-  ( CBan  C_  NrmCVec  ->  ( Rel  NrmCVec  ->  Rel  CBan ) )
52, 3, 4mp2 17 1  |-  Rel  CBan
Colors of variables: wff set class
Syntax hints:    C_ wss 3165   Rel wrel 4710   NrmCVeccnv 21156   CBanccbn 21457
This theorem is referenced by:  hlrel  21485
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277  ax-sep 4157  ax-nul 4165  ax-pr 4230
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-ne 2461  df-rex 2562  df-rab 2565  df-v 2803  df-dif 3168  df-un 3170  df-in 3172  df-ss 3179  df-nul 3469  df-if 3579  df-sn 3659  df-pr 3660  df-op 3662  df-uni 3844  df-br 4040  df-opab 4094  df-xp 4711  df-rel 4712  df-iota 5235  df-fv 5279  df-oprab 5878  df-nv 21164  df-cbn 21458
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