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

Theorem nmcvfval 21277
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 21270 . . 3  |-  normCV  =  2nd
32fveq1i 5609 . 2  |-  ( normCV `  U )  =  ( 2nd `  U )
41, 3eqtri 2378 1  |-  N  =  ( 2nd `  U
)
Colors of variables: wff set class
Syntax hints:    = wceq 1642   ` cfv 5337   2ndc2nd 6208   normCVcnmcv 21260
This theorem is referenced by:  nvop2  21278  nvop  21357  cnnvnm  21364  phop  21510  phpar  21516  h2hnm  21670  hhssnm  21952
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-rex 2625  df-uni 3909  df-br 4105  df-iota 5301  df-fv 5345  df-nmcv 21270
  Copyright terms: Public domain W3C validator