Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ltrn1o | Structured version Visualization version Unicode version |
Description: A lattice translation is a one-to-one onto function. (Contributed by NM, 20-May-2012.) |
Ref | Expression |
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ltrn1o.b | |
ltrn1o.h | |
ltrn1o.t |
Ref | Expression |
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ltrn1o |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpll 790 | . 2 | |
2 | ltrn1o.h | . . 3 | |
3 | eqid 2622 | . . 3 | |
4 | ltrn1o.t | . . 3 | |
5 | 2, 3, 4 | ltrnlaut 35409 | . 2 |
6 | ltrn1o.b | . . 3 | |
7 | 6, 3 | laut1o 35371 | . 2 |
8 | 1, 5, 7 | syl2anc 693 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 wceq 1483 wcel 1990 wf1o 5887 cfv 5888 cbs 15857 clh 35270 claut 35271 cltrn 35387 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-map 7859 df-laut 35275 df-ldil 35390 df-ltrn 35391 |
This theorem is referenced by: ltrncnvnid 35413 ltrncoidN 35414 ltrnid 35421 ltrncnvatb 35424 ltrncnvel 35428 ltrncoval 35431 ltrncnv 35432 ltrneq2 35434 trlcnv 35452 ltrniotacnvval 35870 cdlemg17h 35956 trlcoabs2N 36010 trlcoat 36011 trlcone 36016 cdlemg47a 36022 cdlemg46 36023 cdlemg47 36024 trljco 36028 tgrpgrplem 36037 tendo0pl 36079 tendoipl 36085 cdlemi2 36107 cdlemk2 36120 cdlemk4 36122 cdlemk8 36126 cdlemkid2 36212 cdlemk45 36235 cdlemk53b 36244 cdlemk53 36245 cdlemk55a 36247 tendocnv 36310 dvhgrp 36396 dvhopN 36405 cdlemn3 36486 cdlemn8 36493 cdlemn9 36494 dihordlem7b 36504 dihopelvalcpre 36537 dihmeetlem1N 36579 dihglblem5apreN 36580 |
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