Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eloni 4267 | . . . . 5 | |
2 | ordelsuc 4391 | . . . . 5 | |
3 | 1, 2 | sylan2 284 | . . . 4 |
4 | 3 | rabbidva 2648 | . . 3 |
5 | 4 | inteqd 3746 | . 2 |
6 | sucelon 4389 | . . 3 | |
7 | intmin 3761 | . . 3 | |
8 | 6, 7 | sylbi 120 | . 2 |
9 | 5, 8 | eqtr2d 2151 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wceq 1316 wcel 1465 crab 2397 wss 3041 cint 3741 word 4254 con0 4255 csuc 4257 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 ax-un 4325 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-rab 2402 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-uni 3707 df-int 3742 df-tr 3997 df-iord 4258 df-on 4260 df-suc 4263 |
This theorem is referenced by: (None) |
Copyright terms: Public domain | W3C validator |