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Mirrors > Home > HSE Home > Th. List > elch0 | Structured version Visualization version Unicode version |
Description: Membership in zero for closed subspaces of Hilbert space. (Contributed by NM, 6-Apr-2001.) (New usage is discouraged.) |
Ref | Expression |
---|---|
elch0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ch0 28110 | . . 3 | |
2 | 1 | eleq2i 2693 | . 2 |
3 | ax-hv0cl 27860 | . . . 4 | |
4 | 3 | elexi 3213 | . . 3 |
5 | 4 | elsn2 4211 | . 2 |
6 | 2, 5 | bitri 264 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wb 196 wceq 1483 wcel 1990 csn 4177 chil 27776 c0v 27781 c0h 27792 |
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-hv0cl 27860 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 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-v 3202 df-sn 4178 df-ch0 28110 |
This theorem is referenced by: ocin 28155 ocnel 28157 shuni 28159 choc0 28185 choc1 28186 omlsilem 28261 pjoc1i 28290 shne0i 28307 h1dn0 28411 spansnm0i 28509 nonbooli 28510 eleigvec 28816 cdjreui 29291 cdj3lem1 29293 |
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