Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > onelon | Unicode version |
Description: An element of an ordinal number is an ordinal number. Theorem 2.2(iii) of [BellMachover] p. 469. (Contributed by NM, 26-Oct-2003.) |
Ref | Expression |
---|---|
onelon |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eloni 4130 | . 2 | |
2 | ordelon 4138 | . 2 | |
3 | 1, 2 | sylan 277 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wcel 1433 word 4117 con0 4118 |
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 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-v 2603 df-in 2979 df-ss 2986 df-uni 3602 df-tr 3876 df-iord 4121 df-on 4123 |
This theorem is referenced by: oneli 4183 ssorduni 4231 unon 4255 tfrlemibacc 5963 tfrlemibxssdm 5964 tfrlemibfn 5965 tfrexlem 5971 sucinc2 6049 oav2 6066 omv2 6068 |
Copyright terms: Public domain | W3C validator |