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Mirrors > Home > MPE Home > Th. List > Mathboxes > dalem2 | Structured version Visualization version Unicode version |
Description: Lemma for dath 33346. Show the lines ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
dalema.ph |
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dalemc.l |
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dalemc.j |
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dalemc.a |
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dalem1.o |
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dalem1.y |
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Ref | Expression |
---|---|
dalem2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dalema.ph |
. . . 4
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2 | 1 | dalemkehl 33233 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
3 | 1 | dalempea 33236 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | 1 | dalemqea 33237 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | 1 | dalemsea 33239 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
6 | 1 | dalemtea 33240 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
7 | dalemc.j |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | dalemc.a |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 7, 8 | hlatj4 32984 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 2, 3, 4, 5, 6, 9 | syl122anc 1285 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | dalemc.l |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
12 | dalem1.o |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
13 | dalem1.y |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
14 | 1, 11, 7, 8, 12, 13 | dalempjsen 33263 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 1, 11, 7, 8, 12, 13 | dalemqnet 33262 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | eqid 2462 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 7, 8, 16 | llni2 33122 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | 2, 4, 6, 15, 17 | syl31anc 1279 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | 1, 11, 7, 8, 12, 13 | dalem1 33269 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
20 | 1, 11, 7, 8, 12, 13 | dalemcea 33270 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 1 | dalemclpjs 33244 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 1 | dalemclqjt 33245 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | eqid 2462 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
24 | eqid 2462 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | 11, 23, 24, 8, 16 | 2llnm4 33180 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 2, 20, 14, 18, 21, 22, 25 | syl132anc 1294 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 23, 24, 8, 16 | 2llnmat 33134 |
. . . 4
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28 | 2, 14, 18, 19, 26, 27 | syl32anc 1284 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
29 | 7, 23, 8, 16, 12 | 2llnmj 33170 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
30 | 2, 14, 18, 29 | syl3anc 1276 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
31 | 28, 30 | mpbid 215 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 10, 31 | eqeltrd 2540 |
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 1680 ax-4 1693 ax-5 1769 ax-6 1816 ax-7 1862 ax-8 1900 ax-9 1907 ax-10 1926 ax-11 1931 ax-12 1944 ax-13 2102 ax-ext 2442 ax-rep 4529 ax-sep 4539 ax-nul 4548 ax-pow 4595 ax-pr 4653 ax-un 6610 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3an 993 df-tru 1458 df-ex 1675 df-nf 1679 df-sb 1809 df-eu 2314 df-mo 2315 df-clab 2449 df-cleq 2455 df-clel 2458 df-nfc 2592 df-ne 2635 df-ral 2754 df-rex 2755 df-reu 2756 df-rab 2758 df-v 3059 df-sbc 3280 df-csb 3376 df-dif 3419 df-un 3421 df-in 3423 df-ss 3430 df-nul 3744 df-if 3894 df-pw 3965 df-sn 3981 df-pr 3983 df-op 3987 df-uni 4213 df-iun 4294 df-br 4417 df-opab 4476 df-mpt 4477 df-id 4768 df-xp 4859 df-rel 4860 df-cnv 4861 df-co 4862 df-dm 4863 df-rn 4864 df-res 4865 df-ima 4866 df-iota 5565 df-fun 5603 df-fn 5604 df-f 5605 df-f1 5606 df-fo 5607 df-f1o 5608 df-fv 5609 df-riota 6277 df-ov 6318 df-oprab 6319 df-preset 16222 df-poset 16240 df-plt 16253 df-lub 16269 df-glb 16270 df-join 16271 df-meet 16272 df-p0 16334 df-lat 16341 df-clat 16403 df-oposet 32787 df-ol 32789 df-oml 32790 df-covers 32877 df-ats 32878 df-atl 32909 df-cvlat 32933 df-hlat 32962 df-llines 33108 df-lplanes 33109 |
This theorem is referenced by: dalemdea 33272 |
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