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Mirrors > Home > MPE Home > Th. List > Mathboxes > cdlemksat | Structured version Visualization version Unicode version |
Description: Part of proof of Lemma K of [Crawley] p. 118. (Contributed by NM, 27-Jun-2013.) |
Ref | Expression |
---|---|
cdlemk.b |
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cdlemk.l |
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cdlemk.j |
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cdlemk.a |
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cdlemk.h |
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cdlemk.t |
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cdlemk.r |
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cdlemk.m |
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cdlemk.s |
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Ref | Expression |
---|---|
cdlemksat |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp11 1044 |
. 2
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2 | cdlemk.b |
. . 3
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3 | cdlemk.l |
. . 3
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4 | cdlemk.j |
. . 3
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5 | cdlemk.a |
. . 3
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6 | cdlemk.h |
. . 3
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7 | cdlemk.t |
. . 3
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8 | cdlemk.r |
. . 3
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9 | cdlemk.m |
. . 3
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10 | cdlemk.s |
. . 3
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11 | 2, 3, 4, 5, 6, 7, 8, 9, 10 | cdlemksel 34458 |
. 2
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12 | simp22l 1133 |
. 2
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13 | 3, 5, 6, 7 | ltrnat 33751 |
. 2
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14 | 1, 11, 12, 13 | syl3anc 1276 |
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 4531 ax-sep 4541 ax-nul 4550 ax-pow 4598 ax-pr 4656 ax-un 6615 ax-riotaBAD 32571 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 992 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-nel 2636 df-ral 2754 df-rex 2755 df-reu 2756 df-rmo 2757 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-iin 4295 df-br 4419 df-opab 4478 df-mpt 4479 df-id 4771 df-xp 4862 df-rel 4863 df-cnv 4864 df-co 4865 df-dm 4866 df-rn 4867 df-res 4868 df-ima 4869 df-iota 5569 df-fun 5607 df-fn 5608 df-f 5609 df-f1 5610 df-fo 5611 df-f1o 5612 df-fv 5613 df-riota 6282 df-ov 6323 df-oprab 6324 df-mpt2 6325 df-1st 6825 df-2nd 6826 df-undef 7051 df-map 7505 df-preset 16228 df-poset 16246 df-plt 16259 df-lub 16275 df-glb 16276 df-join 16277 df-meet 16278 df-p0 16340 df-p1 16341 df-lat 16347 df-clat 16409 df-oposet 32788 df-ol 32790 df-oml 32791 df-covers 32878 df-ats 32879 df-atl 32910 df-cvlat 32934 df-hlat 32963 df-llines 33109 df-lplanes 33110 df-lvols 33111 df-lines 33112 df-psubsp 33114 df-pmap 33115 df-padd 33407 df-lhyp 33599 df-laut 33600 df-ldil 33715 df-ltrn 33716 df-trl 33771 |
This theorem is referenced by: cdlemk7 34461 cdlemk11 34462 cdlemk12 34463 cdlemk14 34467 cdlemk15 34468 |
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