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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > ncvr1 | Structured version Visualization version Unicode version |
Description: No element covers the lattice unit. (Contributed by NM, 8-Jul-2013.) |
Ref | Expression |
---|---|
ncvr1.b |
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ncvr1.u |
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ncvr1.c |
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Ref | Expression |
---|---|
ncvr1 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ncvr1.b |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
2 | eqid 2451 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
3 | ncvr1.u |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4 | 1, 2, 3 | ople1 32757 |
. . 3
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5 | opposet 32747 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | 5 | ad2antrr 732 |
. . . . 5
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7 | 1, 3 | op1cl 32751 |
. . . . . 6
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8 | 7 | ad2antrr 732 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | simplr 762 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | simpr 463 |
. . . . 5
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11 | eqid 2451 |
. . . . . 6
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12 | 1, 2, 11 | pltnle 16212 |
. . . . 5
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13 | 6, 8, 9, 10, 12 | syl31anc 1271 |
. . . 4
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14 | 13 | ex 436 |
. . 3
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15 | 4, 14 | mt2d 121 |
. 2
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16 | simpll 760 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
17 | 7 | ad2antrr 732 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
18 | simplr 762 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
19 | simpr 463 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | ncvr1.c |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
21 | 1, 11, 20 | cvrlt 32836 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 16, 17, 18, 19, 21 | syl31anc 1271 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 15, 22 | mtand 665 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-rep 4515 ax-sep 4525 ax-nul 4534 ax-pow 4581 ax-pr 4639 ax-un 6583 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-reu 2744 df-rab 2746 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-pw 3953 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-iun 4280 df-br 4403 df-opab 4462 df-mpt 4463 df-id 4749 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-iota 5546 df-fun 5584 df-fn 5585 df-f 5586 df-f1 5587 df-fo 5588 df-f1o 5589 df-fv 5590 df-riota 6252 df-ov 6293 df-preset 16173 df-poset 16191 df-plt 16204 df-lub 16220 df-p1 16286 df-oposet 32742 df-covers 32832 |
This theorem is referenced by: lhp2lt 33566 |
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