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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 |
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hlnvi.1 |
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Ref | Expression |
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hlnvi |
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Step | Hyp | Ref | Expression |
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1 | hlnvi.1 |
. 2
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2 | hlnv 26599 |
. 2
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3 | 1, 2 | ax-mp 5 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-rex 2755 df-rab 2758 df-v 3059 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4213 df-br 4419 df-iota 5569 df-fv 5613 df-cbn 26561 df-hlo 26594 |
This theorem is referenced by: htthlem 26626 axhfvadd-zf 26691 axhvcom-zf 26692 axhvass-zf 26693 axhvaddid-zf 26695 axhfvmul-zf 26696 axhvmulid-zf 26697 axhvmulass-zf 26698 axhvdistr1-zf 26699 axhvdistr2-zf 26700 axhvmul0-zf 26701 axhis2-zf 26704 axhis3-zf 26705 axhcompl-zf 26707 hilcompl 26910 |
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