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Theorem nmcvfval 30627
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 30620 . . 3 normCV = 2nd
32fveq1i 6906 . 2 (normCV𝑈) = (2nd𝑈)
41, 3eqtri 2764 1 𝑁 = (2nd𝑈)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  cfv 6560  2nd c2nd 8014  normCVcnmcv 30610
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707
This theorem depends on definitions:  df-bi 207  df-an 396  df-tru 1542  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-ss 3967  df-uni 4907  df-br 5143  df-iota 6513  df-fv 6568  df-nmcv 30620
This theorem is referenced by:  nvop2  30628  nvop  30696  cnnvnm  30701  phop  30838  h2hnm  30996  hhssnm  31279
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