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Theorem nmcvfval 22091
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 22084 . . 3  |-  normCV  =  2nd
32fveq1i 5732 . 2  |-  ( normCV `  U )  =  ( 2nd `  U )
41, 3eqtri 2458 1  |-  N  =  ( 2nd `  U
)
Colors of variables: wff set class
Syntax hints:    = wceq 1653   ` cfv 5457   2ndc2nd 6351   normCVcnmcv 22074
This theorem is referenced by:  nvop2  22092  nvop  22171  cnnvnm  22178  phop  22324  phpar  22330  h2hnm  22484  hhssnm  22766
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-rex 2713  df-uni 4018  df-br 4216  df-iota 5421  df-fv 5465  df-nmcv 22084
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