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Mirrors > Home > MPE Home > Th. List > Mathboxes > dihmeetbN | Structured version Unicode version |
Description: Isomorphism H of a
lattice meet when one element is under the fiducial
hyperplane ![]() |
Ref | Expression |
---|---|
dihmeetc.b |
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dihmeetc.l |
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dihmeetc.m |
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dihmeetc.h |
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dihmeetc.i |
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Ref | Expression |
---|---|
dihmeetbN |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl1 991 |
. . 3
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2 | simpl2 992 |
. . 3
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3 | simpr 461 |
. . 3
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4 | simpl3 993 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | dihmeetc.b |
. . . 4
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6 | dihmeetc.m |
. . . 4
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7 | dihmeetc.h |
. . . 4
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8 | dihmeetc.i |
. . . 4
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9 | dihmeetc.l |
. . . 4
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10 | eqid 2454 |
. . . 4
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11 | eqid 2454 |
. . . 4
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12 | eqid 2454 |
. . . 4
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13 | eqid 2454 |
. . . 4
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14 | eqid 2454 |
. . . 4
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15 | eqid 2454 |
. . . 4
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16 | eqid 2454 |
. . . 4
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17 | eqid 2454 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 | dihmeetlem2N 35267 |
. . 3
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19 | 1, 2, 3, 4, 18 | syl121anc 1224 |
. 2
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20 | simpl1 991 |
. . 3
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21 | simpl2 992 |
. . 3
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22 | simpr 461 |
. . 3
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23 | simpl3 993 |
. . 3
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24 | 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17 | dihmeetlem1N 35258 |
. . 3
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25 | 20, 21, 22, 23, 24 | syl121anc 1224 |
. 2
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26 | 19, 25 | pm2.61dan 789 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-rep 4510 ax-sep 4520 ax-nul 4528 ax-pow 4577 ax-pr 4638 ax-un 6481 ax-cnex 9448 ax-resscn 9449 ax-1cn 9450 ax-icn 9451 ax-addcl 9452 ax-addrcl 9453 ax-mulcl 9454 ax-mulrcl 9455 ax-mulcom 9456 ax-addass 9457 ax-mulass 9458 ax-distr 9459 ax-i2m1 9460 ax-1ne0 9461 ax-1rid 9462 ax-rnegex 9463 ax-rrecex 9464 ax-cnre 9465 ax-pre-lttri 9466 ax-pre-lttrn 9467 ax-pre-ltadd 9468 ax-pre-mulgt0 9469 ax-riotaBAD 32927 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3or 966 df-3an 967 df-tru 1373 df-fal 1376 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2266 df-mo 2267 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2649 df-nel 2650 df-ral 2803 df-rex 2804 df-reu 2805 df-rmo 2806 df-rab 2807 df-v 3078 df-sbc 3293 df-csb 3395 df-dif 3438 df-un 3440 df-in 3442 df-ss 3449 df-pss 3451 df-nul 3745 df-if 3899 df-pw 3969 df-sn 3985 df-pr 3987 df-tp 3989 df-op 3991 df-uni 4199 df-int 4236 df-iun 4280 df-iin 4281 df-br 4400 df-opab 4458 df-mpt 4459 df-tr 4493 df-eprel 4739 df-id 4743 df-po 4748 df-so 4749 df-fr 4786 df-we 4788 df-ord 4829 df-on 4830 df-lim 4831 df-suc 4832 df-xp 4953 df-rel 4954 df-cnv 4955 df-co 4956 df-dm 4957 df-rn 4958 df-res 4959 df-ima 4960 df-iota 5488 df-fun 5527 df-fn 5528 df-f 5529 df-f1 5530 df-fo 5531 df-f1o 5532 df-fv 5533 df-riota 6160 df-ov 6202 df-oprab 6203 df-mpt2 6204 df-om 6586 df-1st 6686 df-2nd 6687 df-tpos 6854 df-undef 6901 df-recs 6941 df-rdg 6975 df-1o 7029 df-oadd 7033 df-er 7210 df-map 7325 df-en 7420 df-dom 7421 df-sdom 7422 df-fin 7423 df-pnf 9530 df-mnf 9531 df-xr 9532 df-ltxr 9533 df-le 9534 df-sub 9707 df-neg 9708 df-nn 10433 df-2 10490 df-3 10491 df-4 10492 df-5 10493 df-6 10494 df-n0 10690 df-z 10757 df-uz 10972 df-fz 11554 df-struct 14293 df-ndx 14294 df-slot 14295 df-base 14296 df-sets 14297 df-ress 14298 df-plusg 14369 df-mulr 14370 df-sca 14372 df-vsca 14373 df-0g 14498 df-poset 15234 df-plt 15246 df-lub 15262 df-glb 15263 df-join 15264 df-meet 15265 df-p0 15327 df-p1 15328 df-lat 15334 df-clat 15396 df-mnd 15533 df-submnd 15583 df-grp 15663 df-minusg 15664 df-sbg 15665 df-subg 15796 df-cntz 15953 df-lsm 16255 df-cmn 16399 df-abl 16400 df-mgp 16713 df-ur 16725 df-rng 16769 df-oppr 16837 df-dvdsr 16855 df-unit 16856 df-invr 16886 df-dvr 16897 df-drng 16956 df-lmod 17072 df-lss 17136 df-lsp 17175 df-lvec 17306 df-oposet 33144 df-ol 33146 df-oml 33147 df-covers 33234 df-ats 33235 df-atl 33266 df-cvlat 33290 df-hlat 33319 df-llines 33465 df-lplanes 33466 df-lvols 33467 df-lines 33468 df-psubsp 33470 df-pmap 33471 df-padd 33763 df-lhyp 33955 df-laut 33956 df-ldil 34071 df-ltrn 34072 df-trl 34126 df-tendo 34722 df-edring 34724 df-disoa 34997 df-dvech 35047 df-dib 35107 df-dic 35141 df-dih 35197 |
This theorem is referenced by: dihmeetbclemN 35272 dihmeetALTN 35295 |
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