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

Theorem nmcvfval 25698
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  =  ( normCV `  U )
Assertion
Ref Expression
nmcvfval  |-  N  =  ( 2nd `  U
)

Proof of Theorem nmcvfval
StepHypRef Expression
1 nmfval.6 . 2  |-  N  =  ( normCV `  U )
2 df-nmcv 25691 . . 3  |-  normCV  =  2nd
32fveq1i 5849 . 2  |-  ( normCV `  U )  =  ( 2nd `  U )
41, 3eqtri 2483 1  |-  N  =  ( 2nd `  U
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1398   ` cfv 5570   2ndc2nd 6772   normCVcnmcv 25681
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1623  ax-4 1636  ax-5 1709  ax-6 1752  ax-7 1795  ax-10 1842  ax-11 1847  ax-12 1859  ax-13 2004  ax-ext 2432
This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1401  df-ex 1618  df-nf 1622  df-sb 1745  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-rex 2810  df-uni 4236  df-br 4440  df-iota 5534  df-fv 5578  df-nmcv 25691
This theorem is referenced by:  nvop2  25699  nvop  25778  cnnvnm  25785  phop  25931  phpar  25937  h2hnm  26091  hhssnm  26375
  Copyright terms: Public domain W3C validator