MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  nmcvfval Structured version   Visualization version   GIF version

Theorem nmcvfval 29825
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 29818 . . 3 normCV = 2nd
32fveq1i 6882 . 2 (normCV𝑈) = (2nd𝑈)
41, 3eqtri 2761 1 𝑁 = (2nd𝑈)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  cfv 6535  2nd c2nd 7961  normCVcnmcv 29808
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-in 3953  df-ss 3963  df-uni 4905  df-br 5145  df-iota 6487  df-fv 6543  df-nmcv 29818
This theorem is referenced by:  nvop2  29826  nvop  29894  cnnvnm  29899  phop  30036  h2hnm  30194  hhssnm  30477
  Copyright terms: Public domain W3C validator