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Mirrors > Home > ILE Home > Th. List > sucelon | Unicode version |
Description: The successor of an ordinal number is an ordinal number. (Contributed by NM, 9-Sep-2003.) |
Ref | Expression |
---|---|
sucelon |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | suceloni 4284 |
. 2
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2 | eloni 4169 |
. . 3
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3 | elex 2623 |
. . . . 5
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4 | sucexb 4280 |
. . . . 5
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5 | 3, 4 | sylibr 132 |
. . . 4
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6 | elong 4167 |
. . . . 5
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7 | ordsucg 4285 |
. . . . 5
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8 | 6, 7 | bitrd 186 |
. . . 4
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9 | 5, 8 | syl 14 |
. . 3
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10 | 2, 9 | mpbird 165 |
. 2
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11 | 1, 10 | impbii 124 |
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 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-13 1447 ax-14 1448 ax-17 1462 ax-i9 1466 ax-ial 1470 ax-i5r 1471 ax-ext 2067 ax-sep 3925 ax-pow 3977 ax-pr 4003 ax-un 4227 |
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-ral 2360 df-rex 2361 df-v 2616 df-un 2990 df-in 2992 df-ss 2999 df-pw 3411 df-sn 3431 df-pr 3432 df-uni 3631 df-tr 3905 df-iord 4160 df-on 4162 df-suc 4165 |
This theorem is referenced by: onsucmin 4290 onsucuni2 4346 |
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