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Theorem nmcvfval 28688
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 = (normCV𝑈)
Assertion
Ref Expression
nmcvfval 𝑁 = (2nd𝑈)

Proof of Theorem nmcvfval
StepHypRef Expression
1 nmfval.6 . 2 𝑁 = (normCV𝑈)
2 df-nmcv 28681 . . 3 normCV = 2nd
32fveq1i 6718 . 2 (normCV𝑈) = (2nd𝑈)
41, 3eqtri 2765 1 𝑁 = (2nd𝑈)
Colors of variables: wff setvar class
Syntax hints:   = wceq 1543  cfv 6380  2nd c2nd 7760  normCVcnmcv 28671
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1803  ax-4 1817  ax-5 1918  ax-6 1976  ax-7 2016  ax-8 2112  ax-9 2120  ax-ext 2708
This theorem depends on definitions:  df-bi 210  df-an 400  df-tru 1546  df-ex 1788  df-sb 2071  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3410  df-in 3873  df-ss 3883  df-uni 4820  df-br 5054  df-iota 6338  df-fv 6388  df-nmcv 28681
This theorem is referenced by:  nvop2  28689  nvop  28757  cnnvnm  28762  phop  28899  h2hnm  29057  hhssnm  29340
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