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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > dihjatc3 | Structured version Unicode version |
Description: Isomorphism H of join with an atom. (Contributed by NM, 26-Aug-2014.) |
Ref | Expression |
---|---|
dihjatc1.b |
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dihjatc1.l |
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dihjatc1.h |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
dihjatc1.j |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
dihjatc1.m |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
dihjatc1.a |
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dihjatc1.u |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
dihjatc1.s |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
dihjatc1.i |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
dihjatc3 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dihjatc1.b |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | dihjatc1.l |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | dihjatc1.h |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | dihjatc1.j |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | dihjatc1.m |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | dihjatc1.a |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | dihjatc1.u |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | dihjatc1.s |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | dihjatc1.i |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | 1, 2, 3, 4, 5, 6, 7, 8, 9 | dihjatc1 35262 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | simp11 1018 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
12 | 3, 7, 11 | dvhlmod 35061 |
. . . 4
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13 | lmodabl 17098 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 12, 13 | syl 16 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | eqid 2451 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | 15 | lsssssubg 17145 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
17 | 12, 16 | syl 16 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | simp11l 1099 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | hllat 33314 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | 18, 19 | syl 16 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | simp12 1019 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
22 | simp13 1020 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
23 | 1, 5 | latmcl 15324 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 20, 21, 22, 23 | syl3anc 1219 |
. . . . 5
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25 | 1, 3, 9, 7, 15 | dihlss 35201 |
. . . . 5
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26 | 11, 24, 25 | syl2anc 661 |
. . . 4
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27 | 17, 26 | sseldd 3455 |
. . 3
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28 | simp2l 1014 |
. . . . . 6
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29 | 1, 6 | atbase 33240 |
. . . . . 6
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30 | 28, 29 | syl 16 |
. . . . 5
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31 | 1, 3, 9, 7, 15 | dihlss 35201 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 11, 30, 31 | syl2anc 661 |
. . . 4
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33 | 17, 32 | sseldd 3455 |
. . 3
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34 | 8 | lsmcom 16444 |
. . 3
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35 | 14, 27, 33, 34 | syl3anc 1219 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
36 | 10, 35 | eqtr4d 2495 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 1952 ax-ext 2430 ax-rep 4501 ax-sep 4511 ax-nul 4519 ax-pow 4568 ax-pr 4629 ax-un 6472 ax-cnex 9439 ax-resscn 9440 ax-1cn 9441 ax-icn 9442 ax-addcl 9443 ax-addrcl 9444 ax-mulcl 9445 ax-mulrcl 9446 ax-mulcom 9447 ax-addass 9448 ax-mulass 9449 ax-distr 9450 ax-i2m1 9451 ax-1ne0 9452 ax-1rid 9453 ax-rnegex 9454 ax-rrecex 9455 ax-cnre 9456 ax-pre-lttri 9457 ax-pre-lttrn 9458 ax-pre-ltadd 9459 ax-pre-mulgt0 9460 ax-riotaBAD 32910 |
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 2264 df-mo 2265 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ne 2646 df-nel 2647 df-ral 2800 df-rex 2801 df-reu 2802 df-rmo 2803 df-rab 2804 df-v 3070 df-sbc 3285 df-csb 3387 df-dif 3429 df-un 3431 df-in 3433 df-ss 3440 df-pss 3442 df-nul 3736 df-if 3890 df-pw 3960 df-sn 3976 df-pr 3978 df-tp 3980 df-op 3982 df-uni 4190 df-int 4227 df-iun 4271 df-iin 4272 df-br 4391 df-opab 4449 df-mpt 4450 df-tr 4484 df-eprel 4730 df-id 4734 df-po 4739 df-so 4740 df-fr 4777 df-we 4779 df-ord 4820 df-on 4821 df-lim 4822 df-suc 4823 df-xp 4944 df-rel 4945 df-cnv 4946 df-co 4947 df-dm 4948 df-rn 4949 df-res 4950 df-ima 4951 df-iota 5479 df-fun 5518 df-fn 5519 df-f 5520 df-f1 5521 df-fo 5522 df-f1o 5523 df-fv 5524 df-riota 6151 df-ov 6193 df-oprab 6194 df-mpt2 6195 df-om 6577 df-1st 6677 df-2nd 6678 df-tpos 6845 df-undef 6892 df-recs 6932 df-rdg 6966 df-1o 7020 df-oadd 7024 df-er 7201 df-map 7316 df-en 7411 df-dom 7412 df-sdom 7413 df-fin 7414 df-pnf 9521 df-mnf 9522 df-xr 9523 df-ltxr 9524 df-le 9525 df-sub 9698 df-neg 9699 df-nn 10424 df-2 10481 df-3 10482 df-4 10483 df-5 10484 df-6 10485 df-n0 10681 df-z 10748 df-uz 10963 df-fz 11539 df-struct 14278 df-ndx 14279 df-slot 14280 df-base 14281 df-sets 14282 df-ress 14283 df-plusg 14353 df-mulr 14354 df-sca 14356 df-vsca 14357 df-0g 14482 df-poset 15218 df-plt 15230 df-lub 15246 df-glb 15247 df-join 15248 df-meet 15249 df-p0 15311 df-p1 15312 df-lat 15318 df-clat 15380 df-mnd 15517 df-submnd 15567 df-grp 15647 df-minusg 15648 df-sbg 15649 df-subg 15780 df-cntz 15937 df-lsm 16239 df-cmn 16383 df-abl 16384 df-mgp 16697 df-ur 16709 df-rng 16753 df-oppr 16821 df-dvdsr 16839 df-unit 16840 df-invr 16870 df-dvr 16881 df-drng 16940 df-lmod 17056 df-lss 17120 df-lsp 17159 df-lvec 17290 df-oposet 33127 df-ol 33129 df-oml 33130 df-covers 33217 df-ats 33218 df-atl 33249 df-cvlat 33273 df-hlat 33302 df-llines 33448 df-lplanes 33449 df-lvols 33450 df-lines 33451 df-psubsp 33453 df-pmap 33454 df-padd 33746 df-lhyp 33938 df-laut 33939 df-ldil 34054 df-ltrn 34055 df-trl 34109 df-tendo 34705 df-edring 34707 df-disoa 34980 df-dvech 35030 df-dib 35090 df-dic 35124 df-dih 35180 |
This theorem is referenced by: dihjatc 35368 |
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