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Theorem nmcvfval 22043
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 22036 . . 3  |-  normCV  =  2nd
32fveq1i 5692 . 2  |-  ( normCV `  U )  =  ( 2nd `  U )
41, 3eqtri 2428 1  |-  N  =  ( 2nd `  U
)
Colors of variables: wff set class
Syntax hints:    = wceq 1649   ` cfv 5417   2ndc2nd 6311   normCVcnmcv 22026
This theorem is referenced by:  nvop2  22044  nvop  22123  cnnvnm  22130  phop  22276  phpar  22282  h2hnm  22436  hhssnm  22718
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-rex 2676  df-uni 3980  df-br 4177  df-iota 5381  df-fv 5425  df-nmcv 22036
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