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Theorem nvrel 27327
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 27318 . 2 NrmCVec ⊆ (CVecOLD × V)
2 relxp 5193 . 2 Rel (CVecOLD × V)
3 relss 5172 . 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 3189  wss 3559   × cxp 5077  Rel wrel 5084  CVecOLDcvc 27283  NrmCVeccnv 27309
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4746  ax-nul 4754  ax-pr 4872
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-3an 1038  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-rab 2916  df-v 3191  df-dif 3562  df-un 3564  df-in 3566  df-ss 3573  df-nul 3897  df-if 4064  df-sn 4154  df-pr 4156  df-op 4160  df-opab 4679  df-xp 5085  df-rel 5086  df-oprab 6614  df-nv 27317
This theorem is referenced by:  nvop2  27333  nvop  27401  phrel  27540  bnrel  27593
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