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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > hdmapgln2 | Structured version Unicode version |
Description: g-linear property that will be used for inner product. (Contributed by NM, 14-Jun-2015.) |
Ref | Expression |
---|---|
hdmapgln2.h |
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hdmapgln2.u |
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hdmapgln2.v |
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hdmapgln2.p |
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hdmapgln2.t |
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hdmapgln2.r |
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hdmapgln2.b |
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hdmapgln2.q |
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hdmapgln2.m |
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hdmapgln2.s |
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hdmapgln2.g |
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hdmapgln2.k |
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hdmapgln2.x |
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hdmapgln2.y |
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hdmapgln2.z |
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hdmapgln2.a |
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Ref | Expression |
---|---|
hdmapgln2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hdmapgln2.h |
. . 3
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2 | hdmapgln2.u |
. . 3
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3 | hdmapgln2.v |
. . 3
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4 | hdmapgln2.p |
. . 3
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5 | hdmapgln2.r |
. . 3
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6 | hdmapgln2.q |
. . 3
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7 | hdmapgln2.s |
. . 3
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8 | hdmapgln2.k |
. . 3
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9 | hdmapgln2.x |
. . 3
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10 | 1, 2, 8 | dvhlmod 35118 |
. . . 4
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11 | hdmapgln2.a |
. . . 4
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12 | hdmapgln2.y |
. . . 4
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13 | hdmapgln2.t |
. . . . 5
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14 | hdmapgln2.b |
. . . . 5
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15 | 3, 5, 13, 14 | lmodvscl 17098 |
. . . 4
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16 | 10, 11, 12, 15 | syl3anc 1219 |
. . 3
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17 | hdmapgln2.z |
. . 3
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18 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 16, 17 | hdmaplna2 35921 |
. 2
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19 | hdmapgln2.m |
. . . 4
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20 | hdmapgln2.g |
. . . 4
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21 | 1, 2, 3, 13, 5, 14, 19, 7, 20, 8, 9, 12, 11 | hdmapglnm2 35922 |
. . 3
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22 | 21 | oveq1d 6218 |
. 2
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23 | 18, 22 | eqtrd 2495 |
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 4514 ax-sep 4524 ax-nul 4532 ax-pow 4581 ax-pr 4642 ax-un 6485 ax-cnex 9453 ax-resscn 9454 ax-1cn 9455 ax-icn 9456 ax-addcl 9457 ax-addrcl 9458 ax-mulcl 9459 ax-mulrcl 9460 ax-mulcom 9461 ax-addass 9462 ax-mulass 9463 ax-distr 9464 ax-i2m1 9465 ax-1ne0 9466 ax-1rid 9467 ax-rnegex 9468 ax-rrecex 9469 ax-cnre 9470 ax-pre-lttri 9471 ax-pre-lttrn 9472 ax-pre-ltadd 9473 ax-pre-mulgt0 9474 ax-riotaBAD 32967 |
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 2650 df-nel 2651 df-ral 2804 df-rex 2805 df-reu 2806 df-rmo 2807 df-rab 2808 df-v 3080 df-sbc 3295 df-csb 3399 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-pss 3455 df-nul 3749 df-if 3903 df-pw 3973 df-sn 3989 df-pr 3991 df-tp 3993 df-op 3995 df-ot 3997 df-uni 4203 df-int 4240 df-iun 4284 df-iin 4285 df-br 4404 df-opab 4462 df-mpt 4463 df-tr 4497 df-eprel 4743 df-id 4747 df-po 4752 df-so 4753 df-fr 4790 df-we 4792 df-ord 4833 df-on 4834 df-lim 4835 df-suc 4836 df-xp 4957 df-rel 4958 df-cnv 4959 df-co 4960 df-dm 4961 df-rn 4962 df-res 4963 df-ima 4964 df-iota 5492 df-fun 5531 df-fn 5532 df-f 5533 df-f1 5534 df-fo 5535 df-f1o 5536 df-fv 5537 df-riota 6164 df-ov 6206 df-oprab 6207 df-mpt2 6208 df-of 6433 df-om 6590 df-1st 6690 df-2nd 6691 df-tpos 6858 df-undef 6905 df-recs 6945 df-rdg 6979 df-1o 7033 df-oadd 7037 df-er 7214 df-map 7329 df-en 7424 df-dom 7425 df-sdom 7426 df-fin 7427 df-pnf 9535 df-mnf 9536 df-xr 9537 df-ltxr 9538 df-le 9539 df-sub 9712 df-neg 9713 df-nn 10438 df-2 10495 df-3 10496 df-4 10497 df-5 10498 df-6 10499 df-n0 10695 df-z 10762 df-uz 10977 df-fz 11559 df-struct 14298 df-ndx 14299 df-slot 14300 df-base 14301 df-sets 14302 df-ress 14303 df-plusg 14374 df-mulr 14375 df-sca 14377 df-vsca 14378 df-0g 14503 df-mre 14647 df-mrc 14648 df-acs 14650 df-poset 15239 df-plt 15251 df-lub 15267 df-glb 15268 df-join 15269 df-meet 15270 df-p0 15332 df-p1 15333 df-lat 15339 df-clat 15401 df-mnd 15538 df-submnd 15588 df-grp 15668 df-minusg 15669 df-sbg 15670 df-subg 15801 df-cntz 15958 df-oppg 15984 df-lsm 16260 df-cmn 16404 df-abl 16405 df-mgp 16724 df-ur 16736 df-rng 16780 df-oppr 16848 df-dvdsr 16866 df-unit 16867 df-invr 16897 df-dvr 16908 df-drng 16967 df-lmod 17083 df-lss 17147 df-lsp 17186 df-lvec 17317 df-lsatoms 32984 df-lshyp 32985 df-lcv 33027 df-lfl 33066 df-lkr 33094 df-ldual 33132 df-oposet 33184 df-ol 33186 df-oml 33187 df-covers 33274 df-ats 33275 df-atl 33306 df-cvlat 33330 df-hlat 33359 df-llines 33505 df-lplanes 33506 df-lvols 33507 df-lines 33508 df-psubsp 33510 df-pmap 33511 df-padd 33803 df-lhyp 33995 df-laut 33996 df-ldil 34111 df-ltrn 34112 df-trl 34166 df-tgrp 34750 df-tendo 34762 df-edring 34764 df-dveca 35010 df-disoa 35037 df-dvech 35087 df-dib 35147 df-dic 35181 df-dih 35237 df-doch 35356 df-djh 35403 df-lcdual 35595 df-mapd 35633 df-hvmap 35765 df-hdmap1 35802 df-hdmap 35803 df-hgmap 35895 |
This theorem is referenced by: hdmapglem7b 35939 |
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