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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > cdlemn4a | Unicode version |
Description: Part of proof of Lemma N of [Crawley] p. 121 line 32. (Contributed by NM, 24-Feb-2014.) |
Ref | Expression |
---|---|
cdlemn4.b |
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cdlemn4.l |
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cdlemn4.a |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cdlemn4.p |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cdlemn4.h |
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cdlemn4.t |
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cdlemn4.o |
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cdlemn4.u |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cdlemn4.f |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
cdlemn4.g |
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cdlemn4.j |
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cdlemn4a.n |
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cdlemn4a.s |
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Ref | Expression |
---|---|
cdlemn4a |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cdlemn4.b |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | cdlemn4.l |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | cdlemn4.a |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | cdlemn4.p |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | cdlemn4.h |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | cdlemn4.t |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | cdlemn4.o |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | cdlemn4.u |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | cdlemn4.f |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | cdlemn4.g |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | cdlemn4.j |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
12 | eqid 2408 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12 | cdlemn4 31685 |
. . . 4
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14 | 13 | sneqd 3791 |
. . 3
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15 | 14 | fveq2d 5695 |
. 2
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16 | simp1 957 |
. . . 4
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17 | 5, 8, 16 | dvhlmod 31597 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 2, 3, 5, 4 | lhpocnel2 30505 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 18 | 3ad2ant1 978 |
. . . . 5
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20 | simp2 958 |
. . . . 5
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21 | 2, 3, 5, 6, 9 | ltrniotacl 31065 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 16, 19, 20, 21 | syl3anc 1184 |
. . . 4
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23 | eqid 2408 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | 5, 6, 23 | tendoidcl 31255 |
. . . . 5
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25 | 24 | 3ad2ant1 978 |
. . . 4
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26 | eqid 2408 |
. . . . 5
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27 | 5, 6, 23, 8, 26 | dvhelvbasei 31575 |
. . . 4
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28 | 16, 22, 25, 27 | syl12anc 1182 |
. . 3
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29 | 2, 3, 5, 6, 11 | ltrniotacl 31065 |
. . . 4
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30 | 1, 5, 6, 23, 7 | tendo0cl 31276 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 30 | 3ad2ant1 978 |
. . . 4
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32 | 5, 6, 23, 8, 26 | dvhelvbasei 31575 |
. . . 4
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33 | 16, 29, 31, 32 | syl12anc 1182 |
. . 3
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34 | cdlemn4a.n |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
35 | cdlemn4a.s |
. . . 4
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36 | 26, 12, 34, 35 | lspsntri 16128 |
. . 3
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37 | 17, 28, 33, 36 | syl3anc 1184 |
. 2
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38 | 15, 37 | eqsstrd 3346 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem is referenced by: cdlemn5pre 31687 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-3 7 ax-mp 8 ax-gen 1552 ax-5 1563 ax-17 1623 ax-9 1662 ax-8 1683 ax-13 1723 ax-14 1725 ax-6 1740 ax-7 1745 ax-11 1757 ax-12 1946 ax-ext 2389 ax-rep 4284 ax-sep 4294 ax-nul 4302 ax-pow 4341 ax-pr 4367 ax-un 4664 ax-cnex 9006 ax-resscn 9007 ax-1cn 9008 ax-icn 9009 ax-addcl 9010 ax-addrcl 9011 ax-mulcl 9012 ax-mulrcl 9013 ax-mulcom 9014 ax-addass 9015 ax-mulass 9016 ax-distr 9017 ax-i2m1 9018 ax-1ne0 9019 ax-1rid 9020 ax-rnegex 9021 ax-rrecex 9022 ax-cnre 9023 ax-pre-lttri 9024 ax-pre-lttrn 9025 ax-pre-ltadd 9026 ax-pre-mulgt0 9027 |
This theorem depends on definitions: df-bi 178 df-or 360 df-an 361 df-3or 937 df-3an 938 df-tru 1325 df-fal 1326 df-ex 1548 df-nf 1551 df-sb 1656 df-eu 2262 df-mo 2263 df-clab 2395 df-cleq 2401 df-clel 2404 df-nfc 2533 df-ne 2573 df-nel 2574 df-ral 2675 df-rex 2676 df-reu 2677 df-rmo 2678 df-rab 2679 df-v 2922 df-sbc 3126 df-csb 3216 df-dif 3287 df-un 3289 df-in 3291 df-ss 3298 df-pss 3300 df-nul 3593 df-if 3704 df-pw 3765 df-sn 3784 df-pr 3785 df-tp 3786 df-op 3787 df-uni 3980 df-int 4015 df-iun 4059 df-iin 4060 df-br 4177 df-opab 4231 df-mpt 4232 df-tr 4267 df-eprel 4458 df-id 4462 df-po 4467 df-so 4468 df-fr 4505 df-we 4507 df-ord 4548 df-on 4549 df-lim 4550 df-suc 4551 df-om 4809 df-xp 4847 df-rel 4848 df-cnv 4849 df-co 4850 df-dm 4851 df-rn 4852 df-res 4853 df-ima 4854 df-iota 5381 df-fun 5419 df-fn 5420 df-f 5421 df-f1 5422 df-fo 5423 df-f1o 5424 df-fv 5425 df-ov 6047 df-oprab 6048 df-mpt2 6049 df-1st 6312 df-2nd 6313 df-tpos 6442 df-undef 6506 df-riota 6512 df-recs 6596 df-rdg 6631 df-1o 6687 df-oadd 6691 df-er 6868 df-map 6983 df-en 7073 df-dom 7074 df-sdom 7075 df-fin 7076 df-pnf 9082 df-mnf 9083 df-xr 9084 df-ltxr 9085 df-le 9086 df-sub 9253 df-neg 9254 df-nn 9961 df-2 10018 df-3 10019 df-4 10020 df-5 10021 df-6 10022 df-n0 10182 df-z 10243 df-uz 10449 df-fz 11004 df-struct 13430 df-ndx 13431 df-slot 13432 df-base 13433 df-sets 13434 df-ress 13435 df-plusg 13501 df-mulr 13502 df-sca 13504 df-vsca 13505 df-0g 13686 df-poset 14362 df-plt 14374 df-lub 14390 df-glb 14391 df-join 14392 df-meet 14393 df-p0 14427 df-p1 14428 df-lat 14434 df-clat 14496 df-mnd 14649 df-submnd 14698 df-grp 14771 df-minusg 14772 df-sbg 14773 df-subg 14900 df-cntz 15075 df-lsm 15229 df-cmn 15373 df-abl 15374 df-mgp 15608 df-rng 15622 df-ur 15624 df-oppr 15687 df-dvdsr 15705 df-unit 15706 df-invr 15736 df-dvr 15747 df-drng 15796 df-lmod 15911 df-lss 15968 df-lsp 16007 df-lvec 16134 df-oposet 29663 df-ol 29665 df-oml 29666 df-covers 29753 df-ats 29754 df-atl 29785 df-cvlat 29809 df-hlat 29838 df-llines 29984 df-lplanes 29985 df-lvols 29986 df-lines 29987 df-psubsp 29989 df-pmap 29990 df-padd 30282 df-lhyp 30474 df-laut 30475 df-ldil 30590 df-ltrn 30591 df-trl 30645 df-tendo 31241 df-edring 31243 df-dvech 31566 |
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