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Mirrors > Home > ILE Home > Th. List > ordsson | Unicode version |
Description: Any ordinal class is a subclass of the class of ordinal numbers. Corollary 7.15 of [TakeutiZaring] p. 38. (Contributed by NM, 18-May-1994.) |
Ref | Expression |
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ordsson |
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Step | Hyp | Ref | Expression |
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1 | ordelon 4173 |
. . 3
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2 | 1 | ex 113 |
. 2
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3 | 2 | ssrdv 3016 |
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-io 663 ax-5 1377 ax-7 1378 ax-gen 1379 ax-ie1 1423 ax-ie2 1424 ax-8 1436 ax-10 1437 ax-11 1438 ax-i12 1439 ax-bndl 1440 ax-4 1441 ax-17 1460 ax-i9 1464 ax-ial 1468 ax-i5r 1469 ax-ext 2065 |
This theorem depends on definitions: df-bi 115 df-3an 922 df-tru 1288 df-nf 1391 df-sb 1688 df-clab 2070 df-cleq 2076 df-clel 2079 df-nfc 2212 df-ral 2358 df-rex 2359 df-v 2614 df-in 2990 df-ss 2997 df-uni 3628 df-tr 3902 df-iord 4156 df-on 4158 |
This theorem is referenced by: onss 4272 orduni 4274 iordsmo 5992 tfrlemi14d 6028 tfr1onlemssrecs 6034 tfri1dALT 6046 tfrcllemssrecs 6047 ordiso2 6633 |
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