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Theorem nvrel 27687
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 27678 . 2 NrmCVec ⊆ (CVecOLD × V)
2 relxp 5235 . 2 Rel (CVecOLD × V)
3 relss 5315 . 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 3304  wss 3680   × cxp 5216  Rel wrel 5223  CVecOLDcvc 27643  NrmCVeccnv 27669
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704  ax-sep 4889  ax-nul 4897  ax-pr 5011
This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-3an 1074  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-rab 3023  df-v 3306  df-dif 3683  df-un 3685  df-in 3687  df-ss 3694  df-nul 4024  df-if 4195  df-sn 4286  df-pr 4288  df-op 4292  df-opab 4821  df-xp 5224  df-rel 5225  df-oprab 6769  df-nv 27677
This theorem is referenced by:  nvop2  27693  nvop  27761  phrel  27900  bnrel  27953
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