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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 4376 |
. . . 4
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2 | frirrg 4368 |
. . . 4
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3 | 1, 2 | syl3an1 1282 |
. . 3
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4 | 3 | 3expa 1205 |
. 2
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5 | df-3an 982 |
. . 3
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6 | df-wetr 4352 |
. . . . . . . . . 10
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7 | 6 | simprbi 275 |
. . . . . . . . 9
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8 | 7 | adantr 276 |
. . . . . . . 8
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9 | 8 | r19.21bi 2578 |
. . . . . . 7
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10 | 9 | r19.21bi 2578 |
. . . . . 6
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11 | 10 | anasss 399 |
. . . . 5
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12 | 11 | r19.21bi 2578 |
. . . 4
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13 | 12 | anasss 399 |
. . 3
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14 | 5, 13 | sylan2b 287 |
. 2
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15 | 4, 14 | ispod 4322 |
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 ax-sep 4136 |
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-ne 2361 df-ral 2473 df-v 2754 df-dif 3146 df-un 3148 df-in 3150 df-ss 3157 df-sn 3613 df-pr 3614 df-op 3616 df-br 4019 df-po 4314 df-frfor 4349 df-frind 4350 df-wetr 4352 |
This theorem is referenced by: (None) |
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