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Mirrors > Home > ILE Home > Th. List > wetrep | Unicode version |
Description: An epsilon well-ordering is a transitive relation. (Contributed by NM, 22-Apr-1994.) |
Ref | Expression |
---|---|
wetrep |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3an 980 |
. . 3
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2 | df-wetr 4331 |
. . . . . . . . 9
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3 | 2 | simprbi 275 |
. . . . . . . 8
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4 | 3 | r19.21bi 2565 |
. . . . . . 7
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5 | 4 | r19.21bi 2565 |
. . . . . 6
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6 | 5 | anasss 399 |
. . . . 5
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7 | 6 | r19.21bi 2565 |
. . . 4
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8 | 7 | anasss 399 |
. . 3
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9 | 1, 8 | sylan2b 287 |
. 2
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10 | epel 4289 |
. . 3
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11 | epel 4289 |
. . 3
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12 | 10, 11 | anbi12i 460 |
. 2
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13 | epel 4289 |
. 2
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14 | 9, 12, 13 | 3imtr3g 204 |
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-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4206 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-eu 2029 df-mo 2030 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-op 3600 df-br 4001 df-opab 4062 df-eprel 4286 df-wetr 4331 |
This theorem is referenced by: wessep 4574 |
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