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Theorem nvop2 25324
 Description: A normed complex vector space is an ordered pair of a vector space and a norm operation. (Contributed by NM, 28-Nov-2006.) (New usage is discouraged.)
Hypotheses
Ref Expression
nvop2.1
nvop2.6 CV
Assertion
Ref Expression
nvop2

Proof of Theorem nvop2
StepHypRef Expression
1 nvrel 25318 . . 3
2 1st2nd 6841 . . 3
31, 2mpan 670 . 2
4 nvop2.1 . . 3
5 nvop2.6 . . . 4 CV
65nmcvfval 25323 . . 3
74, 6opeq12i 4224 . 2
83, 7syl6eqr 2526 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1379   wcel 1767  cop 4039   wrel 5010  cfv 5594  c1st 6793  c2nd 6794  cnv 25300  CVcnmcv 25306 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-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445  ax-sep 4574  ax-nul 4582  ax-pow 4631  ax-pr 4692  ax-un 6587 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-eu 2279  df-mo 2280  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-ne 2664  df-ral 2822  df-rex 2823  df-rab 2826  df-v 3120  df-sbc 3337  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-uni 4252  df-br 4454  df-opab 4512  df-mpt 4513  df-id 4801  df-xp 5011  df-rel 5012  df-cnv 5013  df-co 5014  df-dm 5015  df-rn 5016  df-iota 5557  df-fun 5596  df-fv 5602  df-oprab 6299  df-1st 6795  df-2nd 6796  df-nv 25308  df-nmcv 25316 This theorem is referenced by:  nvvop  25325  nvi  25330
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