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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > hdmapg | Structured version Unicode version |
Description: Apply the scalar sigma
function (involution) ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
hdmapg.h |
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hdmapg.u |
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hdmapg.v |
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hdmapg.s |
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hdmapg.g |
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hdmapg.k |
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hdmapg.x |
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hdmapg.y |
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Ref | Expression |
---|---|
hdmapg |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | hdmapg.h |
. 2
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2 | eqid 2454 |
. 2
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3 | eqid 2454 |
. 2
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4 | hdmapg.u |
. 2
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5 | hdmapg.v |
. 2
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6 | eqid 2454 |
. 2
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7 | eqid 2454 |
. 2
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8 | eqid 2454 |
. 2
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9 | eqid 2454 |
. 2
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10 | eqid 2454 |
. 2
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11 | eqid 2454 |
. 2
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12 | hdmapg.k |
. 2
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13 | hdmapg.x |
. 2
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14 | eqid 2454 |
. 2
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15 | eqid 2454 |
. 2
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16 | eqid 2454 |
. 2
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17 | hdmapg.s |
. 2
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18 | hdmapg.g |
. 2
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19 | hdmapg.y |
. 2
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20 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 | hdmapglem7 35916 |
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 4512 ax-sep 4522 ax-nul 4530 ax-pow 4579 ax-pr 4640 ax-un 6483 ax-cnex 9450 ax-resscn 9451 ax-1cn 9452 ax-icn 9453 ax-addcl 9454 ax-addrcl 9455 ax-mulcl 9456 ax-mulrcl 9457 ax-mulcom 9458 ax-addass 9459 ax-mulass 9460 ax-distr 9461 ax-i2m1 9462 ax-1ne0 9463 ax-1rid 9464 ax-rnegex 9465 ax-rrecex 9466 ax-cnre 9467 ax-pre-lttri 9468 ax-pre-lttrn 9469 ax-pre-ltadd 9470 ax-pre-mulgt0 9471 ax-riotaBAD 32943 |
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 3397 df-dif 3440 df-un 3442 df-in 3444 df-ss 3451 df-pss 3453 df-nul 3747 df-if 3901 df-pw 3971 df-sn 3987 df-pr 3989 df-tp 3991 df-op 3993 df-ot 3995 df-uni 4201 df-int 4238 df-iun 4282 df-iin 4283 df-br 4402 df-opab 4460 df-mpt 4461 df-tr 4495 df-eprel 4741 df-id 4745 df-po 4750 df-so 4751 df-fr 4788 df-we 4790 df-ord 4831 df-on 4832 df-lim 4833 df-suc 4834 df-xp 4955 df-rel 4956 df-cnv 4957 df-co 4958 df-dm 4959 df-rn 4960 df-res 4961 df-ima 4962 df-iota 5490 df-fun 5529 df-fn 5530 df-f 5531 df-f1 5532 df-fo 5533 df-f1o 5534 df-fv 5535 df-riota 6162 df-ov 6204 df-oprab 6205 df-mpt2 6206 df-of 6431 df-om 6588 df-1st 6688 df-2nd 6689 df-tpos 6856 df-undef 6903 df-recs 6943 df-rdg 6977 df-1o 7031 df-oadd 7035 df-er 7212 df-map 7327 df-en 7422 df-dom 7423 df-sdom 7424 df-fin 7425 df-pnf 9532 df-mnf 9533 df-xr 9534 df-ltxr 9535 df-le 9536 df-sub 9709 df-neg 9710 df-nn 10435 df-2 10492 df-3 10493 df-4 10494 df-5 10495 df-6 10496 df-n0 10692 df-z 10759 df-uz 10974 df-fz 11556 df-struct 14295 df-ndx 14296 df-slot 14297 df-base 14298 df-sets 14299 df-ress 14300 df-plusg 14371 df-mulr 14372 df-sca 14374 df-vsca 14375 df-0g 14500 df-mre 14644 df-mrc 14645 df-acs 14647 df-poset 15236 df-plt 15248 df-lub 15264 df-glb 15265 df-join 15266 df-meet 15267 df-p0 15329 df-p1 15330 df-lat 15336 df-clat 15398 df-mnd 15535 df-submnd 15585 df-grp 15665 df-minusg 15666 df-sbg 15667 df-subg 15798 df-cntz 15955 df-oppg 15981 df-lsm 16257 df-cmn 16401 df-abl 16402 df-mgp 16715 df-ur 16727 df-rng 16771 df-oppr 16839 df-dvdsr 16857 df-unit 16858 df-invr 16888 df-dvr 16899 df-drng 16958 df-lmod 17074 df-lss 17138 df-lsp 17177 df-lvec 17308 df-lsatoms 32960 df-lshyp 32961 df-lcv 33003 df-lfl 33042 df-lkr 33070 df-ldual 33108 df-oposet 33160 df-ol 33162 df-oml 33163 df-covers 33250 df-ats 33251 df-atl 33282 df-cvlat 33306 df-hlat 33335 df-llines 33481 df-lplanes 33482 df-lvols 33483 df-lines 33484 df-psubsp 33486 df-pmap 33487 df-padd 33779 df-lhyp 33971 df-laut 33972 df-ldil 34087 df-ltrn 34088 df-trl 34142 df-tgrp 34726 df-tendo 34738 df-edring 34740 df-dveca 34986 df-disoa 35013 df-dvech 35063 df-dib 35123 df-dic 35157 df-dih 35213 df-doch 35332 df-djh 35379 df-lcdual 35571 df-mapd 35609 df-hvmap 35741 df-hdmap1 35778 df-hdmap 35779 df-hgmap 35871 |
This theorem is referenced by: hlhilphllem 35946 |
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