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Mirrors > Home > ILE Home > Th. List > wepo | Unicode version |
Description: A well-ordering is a partial ordering. (Contributed by Jim Kingdon, 23-Sep-2021.) |
Ref | Expression |
---|---|
wepo |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wefr 4288 |
. . . 4
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2 | frirrg 4280 |
. . . 4
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3 | 1, 2 | syl3an1 1250 |
. . 3
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4 | 3 | 3expa 1182 |
. 2
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5 | df-3an 965 |
. . 3
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6 | df-wetr 4264 |
. . . . . . . . . 10
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7 | 6 | simprbi 273 |
. . . . . . . . 9
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8 | 7 | adantr 274 |
. . . . . . . 8
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9 | 8 | r19.21bi 2523 |
. . . . . . 7
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10 | 9 | r19.21bi 2523 |
. . . . . 6
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11 | 10 | anasss 397 |
. . . . 5
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12 | 11 | r19.21bi 2523 |
. . . 4
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13 | 12 | anasss 397 |
. . 3
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14 | 5, 13 | sylan2b 285 |
. 2
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15 | 4, 14 | ispod 4234 |
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 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-sep 4054 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ne 2310 df-ral 2422 df-v 2691 df-dif 3078 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-po 4226 df-frfor 4261 df-frind 4262 df-wetr 4264 |
This theorem is referenced by: (None) |
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