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Mirrors > Home > MPE Home > Th. List > Mathboxes > dochexmidlem1 | Structured version Unicode version |
Description: Lemma for dochexmid 35421. Holland's proof implicitly requires
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Ref | Expression |
---|---|
dochexmidlem1.h |
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dochexmidlem1.o |
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dochexmidlem1.u |
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dochexmidlem1.v |
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dochexmidlem1.s |
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dochexmidlem1.n |
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dochexmidlem1.p |
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dochexmidlem1.a |
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dochexmidlem1.k |
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dochexmidlem1.x |
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dochexmidlem1.pp |
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dochexmidlem1.qq |
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dochexmidlem1.rr |
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dochexmidlem1.ql |
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dochexmidlem1.rl |
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Ref | Expression |
---|---|
dochexmidlem1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2451 |
. . . . 5
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2 | dochexmidlem1.a |
. . . . 5
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3 | dochexmidlem1.h |
. . . . . 6
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4 | dochexmidlem1.u |
. . . . . 6
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5 | dochexmidlem1.k |
. . . . . 6
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6 | 3, 4, 5 | dvhlmod 35063 |
. . . . 5
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7 | dochexmidlem1.rr |
. . . . 5
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8 | 1, 2, 6, 7 | lsatn0 32952 |
. . . 4
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9 | dochexmidlem1.s |
. . . . . . 7
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10 | 9, 2, 6, 7 | lsatlssel 32950 |
. . . . . 6
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11 | 1, 9 | lssle0 17139 |
. . . . . 6
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12 | 6, 10, 11 | syl2anc 661 |
. . . . 5
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13 | 12 | necon3bbid 2695 |
. . . 4
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14 | 8, 13 | mpbird 232 |
. . 3
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15 | dochexmidlem1.x |
. . . . 5
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16 | dochexmidlem1.o |
. . . . . 6
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17 | 3, 4, 9, 1, 16 | dochnoncon 35344 |
. . . . 5
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18 | 5, 15, 17 | syl2anc 661 |
. . . 4
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19 | 18 | sseq2d 3484 |
. . 3
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20 | 14, 19 | mtbird 301 |
. 2
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21 | dochexmidlem1.ql |
. . . . . 6
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22 | sseq1 3477 |
. . . . . 6
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23 | 21, 22 | syl5ibcom 220 |
. . . . 5
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24 | dochexmidlem1.rl |
. . . . 5
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25 | 23, 24 | jctild 543 |
. . . 4
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26 | ssin 3672 |
. . . 4
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27 | 25, 26 | syl6ib 226 |
. . 3
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28 | 27 | necon3bd 2660 |
. 2
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29 | 20, 28 | mpd 15 |
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 1952 ax-ext 2430 ax-rep 4503 ax-sep 4513 ax-nul 4521 ax-pow 4570 ax-pr 4631 ax-un 6474 ax-cnex 9441 ax-resscn 9442 ax-1cn 9443 ax-icn 9444 ax-addcl 9445 ax-addrcl 9446 ax-mulcl 9447 ax-mulrcl 9448 ax-mulcom 9449 ax-addass 9450 ax-mulass 9451 ax-distr 9452 ax-i2m1 9453 ax-1ne0 9454 ax-1rid 9455 ax-rnegex 9456 ax-rrecex 9457 ax-cnre 9458 ax-pre-lttri 9459 ax-pre-lttrn 9460 ax-pre-ltadd 9461 ax-pre-mulgt0 9462 ax-riotaBAD 32912 |
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 3072 df-sbc 3287 df-csb 3389 df-dif 3431 df-un 3433 df-in 3435 df-ss 3442 df-pss 3444 df-nul 3738 df-if 3892 df-pw 3962 df-sn 3978 df-pr 3980 df-tp 3982 df-op 3984 df-uni 4192 df-int 4229 df-iun 4273 df-iin 4274 df-br 4393 df-opab 4451 df-mpt 4452 df-tr 4486 df-eprel 4732 df-id 4736 df-po 4741 df-so 4742 df-fr 4779 df-we 4781 df-ord 4822 df-on 4823 df-lim 4824 df-suc 4825 df-xp 4946 df-rel 4947 df-cnv 4948 df-co 4949 df-dm 4950 df-rn 4951 df-res 4952 df-ima 4953 df-iota 5481 df-fun 5520 df-fn 5521 df-f 5522 df-f1 5523 df-fo 5524 df-f1o 5525 df-fv 5526 df-riota 6153 df-ov 6195 df-oprab 6196 df-mpt2 6197 df-om 6579 df-1st 6679 df-2nd 6680 df-tpos 6847 df-undef 6894 df-recs 6934 df-rdg 6968 df-1o 7022 df-oadd 7026 df-er 7203 df-map 7318 df-en 7413 df-dom 7414 df-sdom 7415 df-fin 7416 df-pnf 9523 df-mnf 9524 df-xr 9525 df-ltxr 9526 df-le 9527 df-sub 9700 df-neg 9701 df-nn 10426 df-2 10483 df-3 10484 df-4 10485 df-5 10486 df-6 10487 df-n0 10683 df-z 10750 df-uz 10965 df-fz 11541 df-struct 14280 df-ndx 14281 df-slot 14282 df-base 14283 df-sets 14284 df-ress 14285 df-plusg 14355 df-mulr 14356 df-sca 14358 df-vsca 14359 df-0g 14484 df-poset 15220 df-plt 15232 df-lub 15248 df-glb 15249 df-join 15250 df-meet 15251 df-p0 15313 df-p1 15314 df-lat 15320 df-clat 15382 df-mnd 15519 df-submnd 15569 df-grp 15649 df-minusg 15650 df-sbg 15651 df-subg 15782 df-cntz 15939 df-lsm 16241 df-cmn 16385 df-abl 16386 df-mgp 16699 df-ur 16711 df-rng 16755 df-oppr 16823 df-dvdsr 16841 df-unit 16842 df-invr 16872 df-dvr 16883 df-drng 16942 df-lmod 17058 df-lss 17122 df-lsp 17161 df-lvec 17292 df-lsatoms 32929 df-oposet 33129 df-ol 33131 df-oml 33132 df-covers 33219 df-ats 33220 df-atl 33251 df-cvlat 33275 df-hlat 33304 df-llines 33450 df-lplanes 33451 df-lvols 33452 df-lines 33453 df-psubsp 33455 df-pmap 33456 df-padd 33748 df-lhyp 33940 df-laut 33941 df-ldil 34056 df-ltrn 34057 df-trl 34111 df-tendo 34707 df-edring 34709 df-disoa 34982 df-dvech 35032 df-dib 35092 df-dic 35126 df-dih 35182 df-doch 35301 |
This theorem is referenced by: dochexmidlem3 35415 |
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