Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > ordgt0ge1 | Unicode version |
Description: Two ways to express that an ordinal class is positive. (Contributed by NM, 21-Dec-2004.) |
Ref | Expression |
---|---|
ordgt0ge1 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0elon 4352 | . . 3 | |
2 | ordelsuc 4464 | . . 3 | |
3 | 1, 2 | mpan 421 | . 2 |
4 | df-1o 6363 | . . 3 | |
5 | 4 | sseq1i 3154 | . 2 |
6 | 3, 5 | bitr4di 197 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wcel 2128 wss 3102 c0 3394 word 4322 con0 4323 csuc 4325 c1o 6356 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 ax-nul 4090 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-dif 3104 df-un 3106 df-in 3108 df-ss 3115 df-nul 3395 df-pw 3545 df-sn 3566 df-uni 3773 df-tr 4063 df-iord 4326 df-on 4328 df-suc 4331 df-1o 6363 |
This theorem is referenced by: ordge1n0im 6383 archnqq 7337 |
Copyright terms: Public domain | W3C validator |