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Mirrors > Home > MPE Home > Th. List > latjlej2 | Structured version Visualization version Unicode version |
Description: Add join to both sides of a lattice ordering. (chlej2i 28333 analog.) (Contributed by NM, 8-Nov-2011.) |
Ref | Expression |
---|---|
latlej.b | |
latlej.l | |
latlej.j |
Ref | Expression |
---|---|
latjlej2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | latlej.b | . . 3 | |
2 | latlej.l | . . 3 | |
3 | latlej.j | . . 3 | |
4 | 1, 2, 3 | latjlej1 17065 | . 2 |
5 | 1, 3 | latjcom 17059 | . . . 4 |
6 | 5 | 3adant3r2 1275 | . . 3 |
7 | 1, 3 | latjcom 17059 | . . . 4 |
8 | 7 | 3adant3r1 1274 | . . 3 |
9 | 6, 8 | breq12d 4666 | . 2 |
10 | 4, 9 | sylibd 229 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wceq 1483 wcel 1990 class class class wbr 4653 cfv 5888 (class class class)co 6650 cbs 15857 cple 15948 cjn 16944 clat 17045 |
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-riota 6611 df-ov 6653 df-oprab 6654 df-poset 16946 df-lub 16974 df-glb 16975 df-join 16976 df-meet 16977 df-lat 17046 |
This theorem is referenced by: latjlej12 17067 cvrat3 34728 2llnjaN 34852 2lplnja 34905 dalawlem3 35159 dalawlem6 35162 dalawlem11 35167 lhpj1 35308 cdleme1 35514 cdleme9 35540 cdleme11g 35552 cdleme28a 35658 cdleme30a 35666 cdleme32c 35731 cdlemi1 36106 cdlemk11 36137 cdlemk11u 36159 cdlemk51 36241 cdlemm10N 36407 cdlemn10 36495 |
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