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Theorem nvrel 28013
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 28004 . 2 NrmCVec ⊆ (CVecOLD × V)
2 relxp 5361 . 2 Rel (CVecOLD × V)
3 relss 5442 . 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 3415  wss 3799   × cxp 5341  Rel wrel 5348  CVecOLDcvc 27969  NrmCVeccnv 27995
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1896  ax-4 1910  ax-5 2011  ax-6 2077  ax-7 2114  ax-9 2175  ax-10 2194  ax-11 2209  ax-12 2222  ax-13 2391  ax-ext 2804  ax-sep 5006  ax-nul 5014  ax-pr 5128
This theorem depends on definitions:  df-bi 199  df-an 387  df-or 881  df-3an 1115  df-tru 1662  df-ex 1881  df-nf 1885  df-sb 2070  df-clab 2813  df-cleq 2819  df-clel 2822  df-nfc 2959  df-rab 3127  df-v 3417  df-dif 3802  df-un 3804  df-in 3806  df-ss 3813  df-nul 4146  df-if 4308  df-sn 4399  df-pr 4401  df-op 4405  df-opab 4937  df-xp 5349  df-rel 5350  df-oprab 6910  df-nv 28003
This theorem is referenced by:  nvop2  28019  nvop  28087  phrel  28226  bnrel  28279
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