Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ontr1 | Unicode version |
Description: Transitive law for ordinal numbers. Theorem 7M(b) of [Enderton] p. 192. (Contributed by NM, 11-Aug-1994.) |
Ref | Expression |
---|---|
ontr1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eloni 4267 | . 2 | |
2 | ordtr1 4280 | . 2 | |
3 | 1, 2 | syl 14 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wcel 1465 word 4254 con0 4255 |
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-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 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-v 2662 df-in 3047 df-ss 3054 df-uni 3707 df-tr 3997 df-iord 4258 df-on 4260 |
This theorem is referenced by: smoiun 6166 nntr2 6367 onunsnss 6773 snon0 6792 ltsopi 7096 prarloclemarch2 7195 pwle2 13120 |
Copyright terms: Public domain | W3C validator |