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Mirrors > Home > ILE Home > Th. List > ltntri | Unicode version |
Description: Negative trichotomy
property for real numbers. It is well known that we
cannot prove real number trichotomy, ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Ref | Expression |
---|---|
ltntri |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpll 527 |
. . . 4
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2 | simplr 528 |
. . . 4
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3 | simpr3 1005 |
. . . 4
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4 | 1, 2, 3 | nltled 8077 |
. . 3
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5 | simpr1 1003 |
. . . 4
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6 | 2, 1, 5 | nltled 8077 |
. . 3
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7 | 1, 2 | letri3d 8072 |
. . 3
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8 | 4, 6, 7 | mpbir2and 944 |
. 2
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9 | simpr2 1004 |
. 2
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10 | 8, 9 | pm2.65da 661 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-in1 614 ax-in2 615 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4121 ax-pow 4174 ax-pr 4209 ax-un 4433 ax-setind 4536 ax-cnex 7901 ax-resscn 7902 ax-pre-ltirr 7922 ax-pre-apti 7925 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-fal 1359 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ne 2348 df-nel 2443 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-dif 3131 df-un 3133 df-in 3135 df-ss 3142 df-pw 3577 df-sn 3598 df-pr 3599 df-op 3601 df-uni 3810 df-br 4004 df-opab 4065 df-xp 4632 df-cnv 4634 df-pnf 7993 df-mnf 7994 df-xr 7995 df-ltxr 7996 df-le 7997 |
This theorem is referenced by: (None) |
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