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Mirrors > Home > HSE Home > Th. List > dfhnorm2 | Structured version Visualization version Unicode version |
Description: Alternate definition of the norm of a vector of Hilbert space. Definition of norm in [Beran] p. 96. (Contributed by NM, 6-Jun-2008.) (Revised by Mario Carneiro, 15-Dec-2013.) (New usage is discouraged.) |
Ref | Expression |
---|---|
dfhnorm2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-hnorm 27825 | . 2 | |
2 | ax-hfi 27936 | . . . . . 6 | |
3 | 2 | fdmi 6052 | . . . . 5 |
4 | 3 | dmeqi 5325 | . . . 4 |
5 | dmxpid 5345 | . . . 4 | |
6 | 4, 5 | eqtr2i 2645 | . . 3 |
7 | eqid 2622 | . . 3 | |
8 | 6, 7 | mpteq12i 4742 | . 2 |
9 | 1, 8 | eqtr4i 2647 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1483 cmpt 4729 cxp 5112 cdm 5114 cfv 5888 (class class class)co 6650 cc 9934 csqrt 13973 chil 27776 csp 27779 cno 27780 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-sep 4781 ax-nul 4789 ax-pr 4906 ax-hfi 27936 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rab 2921 df-v 3202 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-sn 4178 df-pr 4180 df-op 4184 df-br 4654 df-opab 4713 df-mpt 4730 df-xp 5120 df-dm 5124 df-fn 5891 df-f 5892 df-hnorm 27825 |
This theorem is referenced by: normf 27980 normval 27981 hilnormi 28020 |
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