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Mirrors > Home > HSE Home > Th. List > chel | Structured version Unicode version |
Description: A member of a closed subspace of a Hilbert space is a vector. (Contributed by NM, 15-Dec-2004.) (New usage is discouraged.) |
Ref | Expression |
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chel |
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Step | Hyp | Ref | Expression |
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1 | chss 24783 |
. 2
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2 | 1 | sselda 3463 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-sep 4520 ax-hilex 24552 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-rex 2804 df-rab 2807 df-v 3078 df-dif 3438 df-un 3440 df-in 3442 df-ss 3449 df-nul 3745 df-if 3899 df-pw 3969 df-sn 3985 df-pr 3987 df-op 3991 df-uni 4199 df-br 4400 df-opab 4458 df-xp 4953 df-cnv 4955 df-dm 4957 df-rn 4958 df-res 4959 df-ima 4960 df-iota 5488 df-fv 5533 df-ov 6202 df-sh 24760 df-ch 24775 |
This theorem is referenced by: pjhtheu2 24970 pjspansn 25131 pjid 25249 atom1d 25908 sumdmdii 25970 |
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