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Theorem nvrel 26107
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 26098 . 2  |-  NrmCVec  C_  ( CVecOLD  X.  _V )
2 relxp 4953 . 2  |-  Rel  ( CVecOLD  X.  _V )
3 relss 4933 . 2  |-  ( NrmCVec  C_  ( CVecOLD  X.  _V )  ->  ( Rel  ( CVecOLD  X.  _V )  ->  Rel  NrmCVec ) )
41, 2, 3mp2 9 1  |-  Rel  NrmCVec
Colors of variables: wff setvar class
Syntax hints:   _Vcvv 3078    C_ wss 3433    X. cxp 4843   Rel wrel 4850   CVecOLDcvc 26050   NrmCVeccnv 26089
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398  ax-sep 4539  ax-nul 4547  ax-pr 4652
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-rab 2782  df-v 3080  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-sn 3994  df-pr 3996  df-op 4000  df-opab 4476  df-xp 4851  df-rel 4852  df-oprab 6300  df-nv 26097
This theorem is referenced by:  nvop2  26113  nvop  26192  phrel  26342  bnrel  26395
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