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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 26839 | . . 3 ⊢ normCV = 2nd | |
3 | 2 | fveq1i 6104 | . 2 ⊢ (normCV‘𝑈) = (2nd ‘𝑈) |
4 | 1, 3 | eqtri 2632 | 1 ⊢ 𝑁 = (2nd ‘𝑈) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1475 ‘cfv 5804 2nd c2nd 7058 normCVcnmcv 26829 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1713 ax-4 1728 ax-5 1827 ax-6 1875 ax-7 1922 ax-10 2006 ax-11 2021 ax-12 2034 ax-13 2234 ax-ext 2590 |
This theorem depends on definitions: df-bi 196 df-or 384 df-an 385 df-tru 1478 df-ex 1696 df-nf 1701 df-sb 1868 df-clab 2597 df-cleq 2603 df-clel 2606 df-nfc 2740 df-rex 2902 df-uni 4373 df-br 4584 df-iota 5768 df-fv 5812 df-nmcv 26839 |
This theorem is referenced by: nvop2 26847 nvop 26915 cnnvnm 26920 phop 27057 phpar 27063 h2hnm 27217 hhssnm 27500 |
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