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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 4385 |
. . . . . . 7
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2 | 1 | simprbi 275 |
. . . . . 6
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3 | ssralv 3234 |
. . . . . 6
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4 | 2, 3 | syl5 32 |
. . . . 5
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5 | 4 | imp 124 |
. . . 4
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6 | 5 | anim2i 342 |
. . 3
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7 | 6 | 3impb 1201 |
. 2
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8 | dford3 4385 |
. 2
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9 | 7, 8 | sylibr 134 |
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-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-11 1517 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-ral 2473 df-in 3150 df-ss 3157 df-iord 4384 |
This theorem is referenced by: ordelord 4399 ordin 4403 ssorduni 4504 ordtriexmidlem 4536 ordtri2or2exmidlem 4543 onsucelsucexmidlem 4546 ordsuc 4580 |
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