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Mirrors > Home > ILE Home > Th. List > sotricim | Unicode version |
Description: One direction of sotritric 4342 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 4335 |
. . . . . . 7
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2 | 1 | adantrr 479 |
. . . . . 6
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3 | 2 | 3adant3 1019 |
. . . . 5
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4 | breq2 4022 |
. . . . . . 7
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5 | 4 | biimprcd 160 |
. . . . . 6
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6 | 5 | 3ad2ant3 1022 |
. . . . 5
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7 | 3, 6 | mtod 664 |
. . . 4
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8 | 7 | 3expia 1207 |
. . 3
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9 | so2nr 4339 |
. . . 4
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10 | imnan 691 |
. . . 4
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11 | 9, 10 | sylibr 134 |
. . 3
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12 | 8, 11 | jcad 307 |
. 2
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13 | ioran 753 |
. 2
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14 | 12, 13 | imbitrrdi 162 |
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 615 ax-in2 616 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-ral 2473 df-v 2754 df-un 3148 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-po 4314 df-iso 4315 |
This theorem is referenced by: sotritric 4342 |
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