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Mirrors > Home > MPE Home > Th. List > cphlmod | Structured version Visualization version Unicode version |
Description: A complex pre-Hilbert space is a left module. (Contributed by Mario Carneiro, 7-Oct-2015.) |
Ref | Expression |
---|---|
cphlmod |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cphnlm 22205 |
. 2
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2 | nlmlmod 21736 |
. 2
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3 | 1, 2 | syl 17 |
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 ax-nul 4550 |
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-eu 2314 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-rab 2758 df-v 3059 df-sbc 3280 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-opab 4478 df-mpt 4479 df-xp 4862 df-cnv 4864 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 df-iota 5569 df-fv 5613 df-ov 6323 df-nlm 21656 df-cph 22201 |
This theorem is referenced by: cphclm 22222 cph2ass 22245 cphtchnm 22259 nmparlem 22268 minveclem1 22421 minveclem2 22423 minveclem4 22429 minveclem6 22431 minveclem2OLD 22435 minveclem4OLD 22441 minveclem6OLD 22443 pjthlem1 22446 pjthlem2 22447 |
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