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Mirrors > Home > HSE Home > Th. List > ela | Unicode version |
Description: Atoms in a Hilbert lattice are the elements that cover the zero subspace. Definition of atom in [Kalmbach] p. 15. (Contributed by NM, 9-Jun-2004.) (New usage is discouraged.) |
Ref | Expression |
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ela |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq2 4180 |
. 2
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2 | df-at 23798 |
. 2
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3 | 1, 2 | elrab2 3058 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: elat2 23800 elatcv0 23801 atcv0 23802 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2389 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3an 938 df-tru 1325 df-ex 1548 df-nf 1551 df-sb 1656 df-clab 2395 df-cleq 2401 df-clel 2404 df-nfc 2533 df-rab 2679 df-v 2922 df-dif 3287 df-un 3289 df-in 3291 df-ss 3298 df-nul 3593 df-if 3704 df-sn 3784 df-pr 3785 df-op 3787 df-br 4177 df-at 23798 |
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