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Mirrors > Home > MPE Home > Th. List > Mathboxes > hlpos | Structured version Visualization version Unicode version |
Description: A Hilbert lattice is a poset. (Contributed by NM, 20-Oct-2011.) |
Ref | Expression |
---|---|
hlpos |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hllat 34650 | . 2 | |
2 | latpos 17050 | . 2 | |
3 | 1, 2 | syl 17 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wcel 1990 cpo 16940 clat 17045 chlt 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-ne 2795 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-opab 4713 df-xp 5120 df-dm 5124 df-iota 5851 df-fv 5896 df-ov 6653 df-lat 17046 df-atl 34585 df-cvlat 34609 df-hlat 34638 |
This theorem is referenced by: hlhgt2 34675 hl0lt1N 34676 cvrval3 34699 cvrexchlem 34705 cvratlem 34707 cvrat 34708 atlelt 34724 2atlt 34725 athgt 34742 1cvratex 34759 ps-2 34764 llnnleat 34799 llncmp 34808 2llnmat 34810 lplnnle2at 34827 llncvrlpln 34844 lplncmp 34848 lvolnle3at 34868 lplncvrlvol 34902 lvolcmp 34903 pmaple 35047 2lnat 35070 2atm2atN 35071 lhp2lt 35287 lhp0lt 35289 dia2dimlem2 36354 dia2dimlem3 36355 dih1 36575 |
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