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Mirrors > Home > MPE Home > Th. List > Mathboxes > poml5N | Structured version Visualization version Unicode version |
Description: Orthomodular law for projective lattices. (Contributed by NM, 23-Mar-2012.) (New usage is discouraged.) |
Ref | Expression |
---|---|
poml4.a | |
poml4.p |
Ref | Expression |
---|---|
poml5N |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1 1061 | . . 3 | |
2 | simp3 1063 | . . . 4 | |
3 | poml4.a | . . . . . 6 | |
4 | poml4.p | . . . . . 6 | |
5 | 3, 4 | polssatN 35194 | . . . . 5 |
6 | 5 | 3adant3 1081 | . . . 4 |
7 | 2, 6 | sstrd 3613 | . . 3 |
8 | 1, 7, 6 | 3jca 1242 | . 2 |
9 | 3, 4 | 3polN 35202 | . . . 4 |
10 | 9 | 3adant3 1081 | . . 3 |
11 | 2, 10 | jca 554 | . 2 |
12 | 3, 4 | poml4N 35239 | . 2 |
13 | 8, 11, 12 | sylc 65 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wceq 1483 wcel 1990 cin 3573 wss 3574 cfv 5888 catm 34550 chlt 34637 cpolN 35188 |
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-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 ax-riotaBAD 34239 |
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-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-nel 2898 df-ral 2917 df-rex 2918 df-reu 2919 df-rmo 2920 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 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-iun 4522 df-iin 4523 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-riota 6611 df-ov 6653 df-oprab 6654 df-undef 7399 df-preset 16928 df-poset 16946 df-plt 16958 df-lub 16974 df-glb 16975 df-join 16976 df-meet 16977 df-p0 17039 df-p1 17040 df-lat 17046 df-clat 17108 df-oposet 34463 df-ol 34465 df-oml 34466 df-covers 34553 df-ats 34554 df-atl 34585 df-cvlat 34609 df-hlat 34638 df-psubsp 34789 df-pmap 34790 df-polarityN 35189 |
This theorem is referenced by: osumcllem3N 35244 |
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