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Mirrors > Home > ILE Home > Th. List > pitric | Unicode version |
Description: Trichotomy for positive integers. (Contributed by Jim Kingdon, 21-Sep-2019.) |
Ref | Expression |
---|---|
pitric |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pinn 6499 | . . 3 | |
2 | pinn 6499 | . . 3 | |
3 | nntri2 6096 | . . 3 | |
4 | 1, 2, 3 | syl2an 283 | . 2 |
5 | ltpiord 6509 | . 2 | |
6 | ltpiord 6509 | . . . . 5 | |
7 | 6 | ancoms 264 | . . . 4 |
8 | 7 | orbi2d 736 | . . 3 |
9 | 8 | notbid 624 | . 2 |
10 | 4, 5, 9 | 3bitr4d 218 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 102 wb 103 wo 661 wceq 1284 wcel 1433 class class class wbr 3785 com 4331 cnpi 6462 clti 6465 |
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-in1 576 ax-in2 577 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-13 1444 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-nul 3904 ax-pow 3948 ax-pr 3964 ax-un 4188 ax-setind 4280 ax-iinf 4329 |
This theorem depends on definitions: df-bi 115 df-3or 920 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-eu 1944 df-mo 1945 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ne 2246 df-ral 2353 df-rex 2354 df-v 2603 df-dif 2975 df-un 2977 df-in 2979 df-ss 2986 df-nul 3252 df-pw 3384 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-int 3637 df-br 3786 df-opab 3840 df-tr 3876 df-eprel 4044 df-iord 4121 df-on 4123 df-suc 4126 df-iom 4332 df-xp 4369 df-ni 6494 df-lti 6497 |
This theorem is referenced by: (None) |
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