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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 4152 |
. . . 4
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2 | frirrg 4144 |
. . . 4
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3 | 1, 2 | syl3an1 1205 |
. . 3
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4 | 3 | 3expa 1141 |
. 2
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5 | df-3an 924 |
. . 3
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6 | df-wetr 4128 |
. . . . . . . . . 10
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7 | 6 | simprbi 269 |
. . . . . . . . 9
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8 | 7 | adantr 270 |
. . . . . . . 8
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9 | 8 | r19.21bi 2457 |
. . . . . . 7
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10 | 9 | r19.21bi 2457 |
. . . . . 6
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11 | 10 | anasss 391 |
. . . . 5
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12 | 11 | r19.21bi 2457 |
. . . 4
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13 | 12 | anasss 391 |
. . 3
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14 | 5, 13 | sylan2b 281 |
. 2
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15 | 4, 14 | ispod 4098 |
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 1379 ax-7 1380 ax-gen 1381 ax-ie1 1425 ax-ie2 1426 ax-8 1438 ax-10 1439 ax-11 1440 ax-i12 1441 ax-bndl 1442 ax-4 1443 ax-17 1462 ax-i9 1466 ax-ial 1470 ax-i5r 1471 ax-ext 2067 ax-sep 3925 |
This theorem depends on definitions: df-bi 115 df-3an 924 df-tru 1290 df-nf 1393 df-sb 1690 df-clab 2072 df-cleq 2078 df-clel 2081 df-nfc 2214 df-ne 2252 df-ral 2360 df-v 2616 df-dif 2988 df-un 2990 df-in 2992 df-ss 2999 df-sn 3431 df-pr 3432 df-op 3434 df-br 3815 df-po 4090 df-frfor 4125 df-frind 4126 df-wetr 4128 |
This theorem is referenced by: (None) |
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