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Mirrors > Home > MPE Home > Th. List > nmcvfval | Structured version Visualization version GIF version |
Description: Value of the norm function in a normed complex vector space. (Contributed by NM, 25-Apr-2007.) (New usage is discouraged.) |
Ref | Expression |
---|---|
nmfval.6 | ⊢ 𝑁 = (normCV‘𝑈) |
Ref | Expression |
---|---|
nmcvfval | ⊢ 𝑁 = (2nd ‘𝑈) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nmfval.6 | . 2 ⊢ 𝑁 = (normCV‘𝑈) | |
2 | df-nmcv 29818 | . . 3 ⊢ normCV = 2nd | |
3 | 2 | fveq1i 6882 | . 2 ⊢ (normCV‘𝑈) = (2nd ‘𝑈) |
4 | 1, 3 | eqtri 2761 | 1 ⊢ 𝑁 = (2nd ‘𝑈) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1542 ‘cfv 6535 2nd c2nd 7961 normCVcnmcv 29808 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1798 ax-4 1812 ax-5 1914 ax-6 1972 ax-7 2012 ax-8 2109 ax-9 2117 ax-ext 2704 |
This theorem depends on definitions: df-bi 206 df-an 398 df-tru 1545 df-ex 1783 df-sb 2069 df-clab 2711 df-cleq 2725 df-clel 2811 df-v 3477 df-in 3953 df-ss 3963 df-uni 4905 df-br 5145 df-iota 6487 df-fv 6543 df-nmcv 29818 |
This theorem is referenced by: nvop2 29826 nvop 29894 cnnvnm 29899 phop 30036 h2hnm 30194 hhssnm 30477 |
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