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Theorem nmcvfval 28311
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 28304 . . 3 normCV = 2nd
32fveq1i 6664 . 2 (normCV𝑈) = (2nd𝑈)
41, 3eqtri 2841 1 𝑁 = (2nd𝑈)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1528  cfv 6348  2nd c2nd 7677  normCVcnmcv 28294
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1787  ax-4 1801  ax-5 1902  ax-6 1961  ax-7 2006  ax-8 2107  ax-9 2115  ax-ext 2790
This theorem depends on definitions:  df-bi 208  df-an 397  df-ex 1772  df-sb 2061  df-clab 2797  df-cleq 2811  df-clel 2890  df-rex 3141  df-uni 4831  df-br 5058  df-iota 6307  df-fv 6356  df-nmcv 28304
This theorem is referenced by:  nvop2  28312  nvop  28380  cnnvnm  28385  phop  28522  h2hnm  28680  hhssnm  28963
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