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Theorem nmcvfval 26846
 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 26839 . . 3 normCV = 2nd
32fveq1i 6104 . 2 (normCV𝑈) = (2nd𝑈)
41, 3eqtri 2632 1 𝑁 = (2nd𝑈)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475  ‘cfv 5804  2nd c2nd 7058  normCVcnmcv 26829 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-rex 2902  df-uni 4373  df-br 4584  df-iota 5768  df-fv 5812  df-nmcv 26839 This theorem is referenced by:  nvop2  26847  nvop  26915  cnnvnm  26920  phop  27057  phpar  27063  h2hnm  27217  hhssnm  27500
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