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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 28304 | . . 3 ⊢ normCV = 2nd | |
3 | 2 | fveq1i 6664 | . 2 ⊢ (normCV‘𝑈) = (2nd ‘𝑈) |
4 | 1, 3 | eqtri 2841 | 1 ⊢ 𝑁 = (2nd ‘𝑈) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1528 ‘cfv 6348 2nd c2nd 7677 normCVcnmcv 28294 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1787 ax-4 1801 ax-5 1902 ax-6 1961 ax-7 2006 ax-8 2107 ax-9 2115 ax-ext 2790 |
This theorem depends on definitions: df-bi 208 df-an 397 df-ex 1772 df-sb 2061 df-clab 2797 df-cleq 2811 df-clel 2890 df-rex 3141 df-uni 4831 df-br 5058 df-iota 6307 df-fv 6356 df-nmcv 28304 |
This theorem is referenced by: nvop2 28312 nvop 28380 cnnvnm 28385 phop 28522 h2hnm 28680 hhssnm 28963 |
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