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Mirrors > Home > ILE Home > Th. List > sotricim | Unicode version |
Description: One direction of sotritric 4115 holds for all weakly linear orders. (Contributed by Jim Kingdon, 28-Sep-2019.) |
Ref | Expression |
---|---|
sotricim |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sonr 4108 |
. . . . . . 7
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2 | 1 | adantrr 463 |
. . . . . 6
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3 | 2 | 3adant3 959 |
. . . . 5
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4 | breq2 3815 |
. . . . . . 7
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5 | 4 | biimprcd 158 |
. . . . . 6
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6 | 5 | 3ad2ant3 962 |
. . . . 5
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7 | 3, 6 | mtod 622 |
. . . 4
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8 | 7 | 3expia 1141 |
. . 3
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9 | so2nr 4112 |
. . . 4
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10 | imnan 657 |
. . . 4
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11 | 9, 10 | sylibr 132 |
. . 3
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12 | 8, 11 | jcad 301 |
. 2
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13 | ioran 702 |
. 2
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14 | 12, 13 | syl6ibr 160 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-in1 577 ax-in2 578 ax-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ral 2358 df-v 2614 df-un 2988 df-sn 3428 df-pr 3429 df-op 3431 df-br 3812 df-po 4087 df-iso 4088 |
This theorem is referenced by: sotritric 4115 |
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