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Mirrors > Home > ILE Home > Th. List > ltpiord | Unicode version |
Description: Positive integer 'less than' in terms of ordinal membership. (Contributed by NM, 6-Feb-1996.) (Revised by Mario Carneiro, 28-Apr-2015.) |
Ref | Expression |
---|---|
ltpiord |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lti 7083 | . . 3 | |
2 | 1 | breqi 3905 | . 2 |
3 | brinxp 4577 | . . 3 | |
4 | epelg 4182 | . . . 4 | |
5 | 4 | adantl 275 | . . 3 |
6 | 3, 5 | bitr3d 189 | . 2 |
7 | 2, 6 | syl5bb 191 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wcel 1465 cin 3040 class class class wbr 3899 cep 4179 cxp 4507 cnpi 7048 clti 7051 |
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-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 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-eu 1980 df-mo 1981 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-rex 2399 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-opab 3960 df-eprel 4181 df-xp 4515 df-lti 7083 |
This theorem is referenced by: ltsopi 7096 pitric 7097 pitri3or 7098 ltdcpi 7099 ltexpi 7113 ltapig 7114 ltmpig 7115 1lt2pi 7116 nlt1pig 7117 archnqq 7193 prarloclemarch2 7195 prarloclemlt 7269 prarloclemn 7275 |
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