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Theorem nmcvfval 28397
 Description: Value of the norm function in a normed complex vector space. (Contributed by NM, 25-Apr-2007.) (New usage is discouraged.)
Hypothesis
Ref Expression
nmfval.6 𝑁 = (normCV𝑈)
Assertion
Ref Expression
nmcvfval 𝑁 = (2nd𝑈)

Proof of Theorem nmcvfval
StepHypRef Expression
1 nmfval.6 . 2 𝑁 = (normCV𝑈)
2 df-nmcv 28390 . . 3 normCV = 2nd
32fveq1i 6646 . 2 (normCV𝑈) = (2nd𝑈)
41, 3eqtri 2821 1 𝑁 = (2nd𝑈)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538  ‘cfv 6324  2nd c2nd 7672  normCVcnmcv 28380 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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-in 3888  df-ss 3898  df-uni 4801  df-br 5031  df-iota 6283  df-fv 6332  df-nmcv 28390 This theorem is referenced by:  nvop2  28398  nvop  28466  cnnvnm  28471  phop  28608  h2hnm  28766  hhssnm  29049
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