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Mirrors > Home > MPE Home > Th. List > Mathboxes > cdlemksel | Structured version Visualization version Unicode version |
Description: Part of proof of Lemma K of [Crawley] p. 118. Conditions for the sigma(p) function to be a translation. TODO: combine cdlemki 34410? (Contributed by NM, 26-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 |
---|---|
cdlemksel |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp13 1041 |
. . 3
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2 | cdlemk.b |
. . . 4
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3 | cdlemk.l |
. . . 4
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4 | cdlemk.j |
. . . 4
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5 | cdlemk.a |
. . . 4
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6 | cdlemk.h |
. . . 4
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7 | cdlemk.t |
. . . 4
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8 | cdlemk.r |
. . . 4
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9 | cdlemk.m |
. . . 4
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10 | cdlemk.s |
. . . 4
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11 | 2, 3, 4, 5, 6, 7, 8, 9, 10 | cdlemksv 34413 |
. . 3
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12 | 1, 11 | syl 17 |
. 2
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13 | eqid 2452 |
. . 3
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14 | 2, 3, 4, 5, 6, 7, 8, 9, 13 | cdlemki 34410 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 12, 14 | eqeltrd 2530 |
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 1673 ax-4 1686 ax-5 1762 ax-6 1809 ax-7 1855 ax-8 1893 ax-9 1900 ax-10 1919 ax-11 1924 ax-12 1937 ax-13 2092 ax-ext 2432 ax-rep 4487 ax-sep 4497 ax-nul 4506 ax-pow 4554 ax-pr 4612 ax-un 6571 ax-riotaBAD 32527 |
This theorem depends on definitions: df-bi 190 df-or 376 df-an 377 df-3or 987 df-3an 988 df-tru 1451 df-ex 1668 df-nf 1672 df-sb 1802 df-eu 2304 df-mo 2305 df-clab 2439 df-cleq 2445 df-clel 2448 df-nfc 2582 df-ne 2624 df-nel 2625 df-ral 2742 df-rex 2743 df-reu 2744 df-rmo 2745 df-rab 2746 df-v 3015 df-sbc 3236 df-csb 3332 df-dif 3375 df-un 3377 df-in 3379 df-ss 3386 df-nul 3700 df-if 3850 df-pw 3921 df-sn 3937 df-pr 3939 df-op 3943 df-uni 4169 df-iun 4250 df-iin 4251 df-br 4375 df-opab 4434 df-mpt 4435 df-id 4727 df-xp 4818 df-rel 4819 df-cnv 4820 df-co 4821 df-dm 4822 df-rn 4823 df-res 4824 df-ima 4825 df-iota 5525 df-fun 5563 df-fn 5564 df-f 5565 df-f1 5566 df-fo 5567 df-f1o 5568 df-fv 5569 df-riota 6238 df-ov 6279 df-oprab 6280 df-mpt2 6281 df-1st 6781 df-2nd 6782 df-undef 7007 df-map 7461 df-preset 16184 df-poset 16202 df-plt 16215 df-lub 16231 df-glb 16232 df-join 16233 df-meet 16234 df-p0 16296 df-p1 16297 df-lat 16303 df-clat 16365 df-oposet 32744 df-ol 32746 df-oml 32747 df-covers 32834 df-ats 32835 df-atl 32866 df-cvlat 32890 df-hlat 32919 df-llines 33065 df-lplanes 33066 df-lvols 33067 df-lines 33068 df-psubsp 33070 df-pmap 33071 df-padd 33363 df-lhyp 33555 df-laut 33556 df-ldil 33671 df-ltrn 33672 df-trl 33727 |
This theorem is referenced by: cdlemksat 34415 cdlemksv2 34416 cdlemk12 34419 cdlemkoatnle 34420 |
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