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Mirrors > Home > ILE Home > Th. List > onsucmin | Unicode version |
Description: The successor of an ordinal number is the smallest larger ordinal number. (Contributed by NM, 28-Nov-2003.) |
Ref | Expression |
---|---|
onsucmin |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eloni 4371 |
. . . . 5
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2 | ordelsuc 4500 |
. . . . 5
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3 | 1, 2 | sylan2 286 |
. . . 4
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4 | 3 | rabbidva 2725 |
. . 3
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5 | 4 | inteqd 3847 |
. 2
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6 | onsucb 4498 |
. . 3
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7 | intmin 3862 |
. . 3
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8 | 6, 7 | sylbi 121 |
. 2
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9 | 5, 8 | eqtr2d 2211 |
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-13 2150 ax-14 2151 ax-ext 2159 ax-sep 4118 ax-pow 4171 ax-pr 4205 ax-un 4429 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2739 df-un 3133 df-in 3135 df-ss 3142 df-pw 3576 df-sn 3597 df-pr 3598 df-uni 3808 df-int 3843 df-tr 4099 df-iord 4362 df-on 4364 df-suc 4367 |
This theorem is referenced by: (None) |
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