Mathbox for Norm Megill |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > Mathboxes > hlcvl | Structured version Visualization version GIF version |
Description: A Hilbert lattice is an atomic lattice with the covering property. (Contributed by NM, 5-Nov-2012.) |
Ref | Expression |
---|---|
hlcvl | ⊢ (𝐾 ∈ HL → 𝐾 ∈ CvLat) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hlomcmcv 34643 | . 2 ⊢ (𝐾 ∈ HL → (𝐾 ∈ OML ∧ 𝐾 ∈ CLat ∧ 𝐾 ∈ CvLat)) | |
2 | 1 | simp3d 1075 | 1 ⊢ (𝐾 ∈ HL → 𝐾 ∈ CvLat) |
Colors of variables: wff setvar class |
Syntax hints: → wi 4 ∈ wcel 1990 CLatccla 17107 OMLcoml 34462 CvLatclc 34552 HLchlt 34637 |
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 |
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-ral 2917 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-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-br 4654 df-iota 5851 df-fv 5896 df-ov 6653 df-hlat 34638 |
This theorem is referenced by: hlatl 34647 hlexch1 34668 hlexch2 34669 hlexchb1 34670 hlexchb2 34671 hlsupr2 34673 hlexch3 34677 hlexch4N 34678 hlatexchb1 34679 hlatexchb2 34680 hlatexch1 34681 hlatexch2 34682 llnexchb2lem 35154 4atexlemkc 35344 4atex 35362 4atex3 35367 cdleme02N 35509 cdleme0ex2N 35511 cdleme0moN 35512 cdleme0nex 35577 cdleme20zN 35588 cdleme20yOLD 35590 cdleme19a 35591 cdleme19d 35594 cdleme21a 35613 cdleme21b 35614 cdleme21c 35615 cdleme21ct 35617 cdleme22f 35634 cdleme22f2 35635 cdleme22g 35636 cdlemf1 35849 |
Copyright terms: Public domain | W3C validator |