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Theorem nvrel 22081
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 22072 . 2  |-  NrmCVec  C_  ( CVec OLD  X.  _V )
2 relxp 4983 . 2  |-  Rel  ( CVec OLD  X.  _V )
3 relss 4963 . 2  |-  ( NrmCVec  C_  ( CVec OLD  X.  _V )  ->  ( Rel  ( CVec
OLD  X.  _V )  ->  Rel  NrmCVec ) )
41, 2, 3mp2 9 1  |-  Rel  NrmCVec
Colors of variables: wff set class
Syntax hints:   _Vcvv 2956    C_ wss 3320    X. cxp 4876   Rel wrel 4883   CVec OLDcvc 22024   NrmCVeccnv 22063
This theorem is referenced by:  nvop2  22087  nvop  22166  phrel  22316  bnrel  22369
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-opab 4267  df-xp 4884  df-rel 4885  df-oprab 6085  df-nv 22071
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