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Theorem nvrel 21158
Description: The class of all normed complex vectors spaces is a relation. (Contributed by NM, 14-Nov-2006.) (New usage is discouraged.)
Assertion
Ref Expression
nvrel  |-  Rel  NrmCVec

Proof of Theorem nvrel
StepHypRef Expression
1 nvss 21149 . 2  |-  NrmCVec  C_  ( CVec OLD  X.  _V )
2 relxp 4794 . 2  |-  Rel  ( CVec OLD  X.  _V )
3 relss 4775 . 2  |-  ( NrmCVec  C_  ( CVec OLD  X.  _V )  ->  ( Rel  ( CVec
OLD  X.  _V )  ->  Rel  NrmCVec ) )
41, 2, 3mp2 17 1  |-  Rel  NrmCVec
Colors of variables: wff set class
Syntax hints:   _Vcvv 2788    C_ wss 3152    X. cxp 4687   Rel wrel 4694   CVec OLDcvc 21101   NrmCVeccnv 21140
This theorem is referenced by:  nvop2  21164  nvop  21243  phrel  21393  bnrel  21446
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-opab 4078  df-xp 4695  df-rel 4696  df-oprab 5862  df-nv 21148
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