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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > lncvrat | Structured version Unicode version |
Description: A line covers the atoms it contains. (Contributed by NM, 30-Apr-2012.) |
Ref | Expression |
---|---|
lncvrat.b |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
lncvrat.l |
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lncvrat.c |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
lncvrat.a |
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lncvrat.n |
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lncvrat.m |
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Ref | Expression |
---|---|
lncvrat |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simprl 755 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | simpl1 991 |
. . . 4
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3 | simpl2 992 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | lncvrat.b |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
5 | eqid 2454 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | lncvrat.a |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | lncvrat.n |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | lncvrat.m |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
9 | 4, 5, 6, 7, 8 | isline3 33783 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
10 | 2, 3, 9 | syl2anc 661 |
. . 3
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11 | 1, 10 | mpbid 210 |
. 2
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12 | simp1l1 1081 |
. . . . . 6
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13 | simp1l3 1083 |
. . . . . 6
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14 | simp2l 1014 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
15 | simp2r 1015 |
. . . . . 6
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16 | simp3l 1016 |
. . . . . 6
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17 | simp1rr 1054 |
. . . . . . 7
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18 | simp3r 1017 |
. . . . . . 7
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19 | 17, 18 | breqtrd 4427 |
. . . . . 6
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20 | lncvrat.l |
. . . . . . 7
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21 | lncvrat.c |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
22 | 20, 5, 21, 6 | atcvrj2 33440 |
. . . . . 6
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23 | 12, 13, 14, 15, 16, 19, 22 | syl132anc 1237 |
. . . . 5
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24 | 23, 18 | breqtrrd 4429 |
. . . 4
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25 | 24 | 3exp 1187 |
. . 3
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26 | 25 | rexlimdvv 2953 |
. 2
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27 | 11, 26 | mpd 15 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-8 1760 ax-9 1762 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1955 ax-ext 2432 ax-rep 4514 ax-sep 4524 ax-nul 4532 ax-pow 4581 ax-pr 4642 ax-un 6485 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-eu 2266 df-mo 2267 df-clab 2440 df-cleq 2446 df-clel 2449 df-nfc 2604 df-ne 2650 df-ral 2804 df-rex 2805 df-reu 2806 df-rab 2808 df-v 3080 df-sbc 3295 df-csb 3399 df-dif 3442 df-un 3444 df-in 3446 df-ss 3453 df-nul 3749 df-if 3903 df-pw 3973 df-sn 3989 df-pr 3991 df-op 3995 df-uni 4203 df-iun 4284 df-br 4404 df-opab 4462 df-mpt 4463 df-id 4747 df-xp 4957 df-rel 4958 df-cnv 4959 df-co 4960 df-dm 4961 df-rn 4962 df-res 4963 df-ima 4964 df-iota 5492 df-fun 5531 df-fn 5532 df-f 5533 df-f1 5534 df-fo 5535 df-f1o 5536 df-fv 5537 df-riota 6164 df-ov 6206 df-oprab 6207 df-poset 15239 df-plt 15251 df-lub 15267 df-glb 15268 df-join 15269 df-meet 15270 df-p0 15332 df-lat 15339 df-clat 15401 df-oposet 33184 df-ol 33186 df-oml 33187 df-covers 33274 df-ats 33275 df-atl 33306 df-cvlat 33330 df-hlat 33359 df-lines 33508 df-pmap 33511 |
This theorem is referenced by: 2lnat 33791 |
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