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Mirrors > Home > ILE Home > Th. List > trssord | Unicode version |
Description: A transitive subclass of an ordinal class is ordinal. (Contributed by NM, 29-May-1994.) |
Ref | Expression |
---|---|
trssord |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dford3 4192 |
. . . . . . 7
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2 | 1 | simprbi 269 |
. . . . . 6
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3 | ssralv 3085 |
. . . . . 6
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4 | 2, 3 | syl5 32 |
. . . . 5
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5 | 4 | imp 122 |
. . . 4
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6 | 5 | anim2i 334 |
. . 3
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7 | 6 | 3impb 1139 |
. 2
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8 | dford3 4192 |
. 2
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9 | 7, 8 | sylibr 132 |
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-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-11 1442 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-ral 2364 df-in 3005 df-ss 3012 df-iord 4191 |
This theorem is referenced by: ordelord 4206 ordin 4210 ssorduni 4302 ordtriexmidlem 4334 ordtri2or2exmidlem 4340 onsucelsucexmidlem 4343 ordsuc 4377 |
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