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Theorem nmcvfval 24132
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 24125 . . 3  |-  normCV  =  2nd
32fveq1i 5795 . 2  |-  ( normCV `  U )  =  ( 2nd `  U )
41, 3eqtri 2481 1  |-  N  =  ( 2nd `  U
)
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370   ` cfv 5521   2ndc2nd 6681   normCVcnmcv 24115
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1954  ax-ext 2431
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2602  df-rex 2802  df-uni 4195  df-br 4396  df-iota 5484  df-fv 5529  df-nmcv 24125
This theorem is referenced by:  nvop2  24133  nvop  24212  cnnvnm  24219  phop  24365  phpar  24371  h2hnm  24525  hhssnm  24809
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