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Mirrors > Home > MPE Home > Th. List > Mathboxes > dalem15 | Structured version Visualization version Unicode version |
Description: Lemma for dath 33345. The axis of perspectivity ![]() |
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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dalem15.m |
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dalem15.n |
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dalem15.o |
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dalem15.y |
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dalem15.z |
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dalem15.x |
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Ref | Expression |
---|---|
dalem15 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dalem15.x |
. 2
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2 | dalema.ph |
. . . 4
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3 | dalemc.l |
. . . 4
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4 | dalemc.j |
. . . 4
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5 | dalemc.a |
. . . 4
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6 | dalem15.o |
. . . 4
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7 | eqid 2461 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | dalem15.y |
. . . 4
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9 | dalem15.z |
. . . 4
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10 | eqid 2461 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | 2, 3, 4, 5, 6, 7, 8, 9, 10 | dalem14 33286 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
12 | 2 | dalemkehl 33232 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | 2 | dalemyeo 33241 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 2 | dalemzeo 33242 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | dalem15.m |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
16 | dalem15.n |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 4, 15, 16, 6, 7 | 2lplnmj 33231 |
. . . . 5
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18 | 12, 13, 14, 17 | syl3anc 1276 |
. . . 4
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19 | 18 | adantr 471 |
. . 3
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20 | 11, 19 | mpbird 240 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 1, 20 | syl5eqel 2543 |
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 1679 ax-4 1692 ax-5 1768 ax-6 1815 ax-7 1861 ax-8 1899 ax-9 1906 ax-10 1925 ax-11 1930 ax-12 1943 ax-13 2101 ax-ext 2441 ax-rep 4528 ax-sep 4538 ax-nul 4547 ax-pow 4594 ax-pr 4652 ax-un 6609 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 df-3an 993 df-tru 1457 df-ex 1674 df-nf 1678 df-sb 1808 df-eu 2313 df-mo 2314 df-clab 2448 df-cleq 2454 df-clel 2457 df-nfc 2591 df-ne 2634 df-ral 2753 df-rex 2754 df-reu 2755 df-rab 2757 df-v 3058 df-sbc 3279 df-csb 3375 df-dif 3418 df-un 3420 df-in 3422 df-ss 3429 df-nul 3743 df-if 3893 df-pw 3964 df-sn 3980 df-pr 3982 df-op 3986 df-uni 4212 df-iun 4293 df-br 4416 df-opab 4475 df-mpt 4476 df-id 4767 df-xp 4858 df-rel 4859 df-cnv 4860 df-co 4861 df-dm 4862 df-rn 4863 df-res 4864 df-ima 4865 df-iota 5564 df-fun 5602 df-fn 5603 df-f 5604 df-f1 5605 df-fo 5606 df-f1o 5607 df-fv 5608 df-riota 6276 df-ov 6317 df-oprab 6318 df-preset 16221 df-poset 16239 df-plt 16252 df-lub 16268 df-glb 16269 df-join 16270 df-meet 16271 df-p0 16333 df-lat 16340 df-clat 16402 df-oposet 32786 df-ol 32788 df-oml 32789 df-covers 32876 df-ats 32877 df-atl 32908 df-cvlat 32932 df-hlat 32961 df-llines 33107 df-lplanes 33108 df-lvols 33109 |
This theorem is referenced by: dalem16 33288 dalem53 33334 |
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