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Mirrors > Home > HSE Home > Th. List > cheli | Structured version Visualization version Unicode version |
Description: A member of a closed subspace of a Hilbert space is a vector. (Contributed by NM, 6-Oct-1999.) (New usage is discouraged.) |
Ref | Expression |
---|---|
chssi.1 |
Ref | Expression |
---|---|
cheli |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | chssi.1 | . . 3 | |
2 | 1 | chssii 28088 | . 2 |
3 | 2 | sseli 3599 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 chil 27776 cch 27786 |
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-hilex 27856 |
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-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-opab 4713 df-xp 5120 df-cnv 5122 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fv 5896 df-ov 6653 df-sh 28064 df-ch 28078 |
This theorem is referenced by: pjhthlem1 28250 pjhthlem2 28251 h1de2ci 28415 spanunsni 28438 spansncvi 28511 3oalem1 28521 pjcompi 28531 pjocini 28557 pjjsi 28559 pjrni 28561 pjdsi 28571 pjds3i 28572 mayete3i 28587 riesz3i 28921 pjnmopi 29007 pjnormssi 29027 pjimai 29035 pjclem4a 29057 pjclem4 29058 pj3lem1 29065 pj3si 29066 strlem1 29109 strlem3 29112 strlem5 29114 hstrlem3 29120 hstrlem5 29122 sumdmdii 29274 sumdmdlem 29277 sumdmdlem2 29278 |
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