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Mirrors > Home > MPE Home > Th. List > hlnvi | Structured version Visualization version Unicode version |
Description: Every complex Hilbert space is a normed complex vector space. (Contributed by NM, 6-Jun-2008.) (New usage is discouraged.) |
Ref | Expression |
---|---|
hlnvi.1 |
Ref | Expression |
---|---|
hlnvi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hlnvi.1 | . 2 | |
2 | hlnv 27747 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wcel 1990 cnv 27439 chlo 27741 |
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 |
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-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-rex 2918 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-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-cbn 27719 df-hlo 27742 |
This theorem is referenced by: htthlem 27774 axhfvadd-zf 27839 axhvcom-zf 27840 axhvass-zf 27841 axhvaddid-zf 27843 axhfvmul-zf 27844 axhvmulid-zf 27845 axhvmulass-zf 27846 axhvdistr1-zf 27847 axhvdistr2-zf 27848 axhvmul0-zf 27849 axhis2-zf 27852 axhis3-zf 27853 axhcompl-zf 27855 hilcompl 28058 |
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