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Theorem nvrel 25268
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 25259 . 2  |-  NrmCVec  C_  ( CVecOLD  X.  _V )
2 relxp 5110 . 2  |-  Rel  ( CVecOLD  X.  _V )
3 relss 5090 . 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 3113    C_ wss 3476    X. cxp 4997   Rel wrel 5004   CVecOLDcvc 25211   NrmCVeccnv 25250
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4568  ax-nul 4576  ax-pr 4686
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-rab 2823  df-v 3115  df-dif 3479  df-un 3481  df-in 3483  df-ss 3490  df-nul 3786  df-if 3940  df-sn 4028  df-pr 4030  df-op 4034  df-opab 4506  df-xp 5005  df-rel 5006  df-oprab 6289  df-nv 25258
This theorem is referenced by:  nvop2  25274  nvop  25353  phrel  25503  bnrel  25556
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