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Theorem nvrel 28388
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 28379 . 2 NrmCVec ⊆ (CVecOLD × V)
2 relxp 5560 . 2 Rel (CVecOLD × V)
3 relss 5643 . 2 (NrmCVec ⊆ (CVecOLD × V) → (Rel (CVecOLD × V) → Rel NrmCVec))
41, 2, 3mp2 9 1 Rel NrmCVec
Colors of variables: wff setvar class
Syntax hints:  Vcvv 3480  wss 3919   × cxp 5540  Rel wrel 5547  CVecOLDcvc 28344  NrmCVeccnv 28370
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-10 2146  ax-11 2162  ax-12 2179  ax-ext 2796  ax-sep 5189  ax-nul 5196  ax-pr 5317
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-tru 1541  df-ex 1782  df-nf 1786  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-nfc 2964  df-v 3482  df-dif 3922  df-un 3924  df-in 3926  df-ss 3936  df-nul 4277  df-if 4451  df-sn 4551  df-pr 4553  df-op 4557  df-opab 5115  df-xp 5548  df-rel 5549  df-oprab 7153  df-nv 28378
This theorem is referenced by:  nvop2  28394  nvop  28462  phrel  28601  bnrel  28653
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