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Theorem nmcvfval 21163
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 21156 . . 3  |-  normCV  =  2nd
32fveq1i 5526 . 2  |-  ( normCV `  U )  =  ( 2nd `  U )
41, 3eqtri 2303 1  |-  N  =  ( 2nd `  U
)
Colors of variables: wff set class
Syntax hints:    = wceq 1623   ` cfv 5255   2ndc2nd 6121   normCVcnmcv 21146
This theorem is referenced by:  nvop2  21164  nvop  21243  cnnvnm  21250  phop  21396  phpar  21402  h2hnm  21556  hhssnm  21838
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-rex 2549  df-uni 3828  df-br 4024  df-iota 5219  df-fv 5263  df-nmcv 21156
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