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Mirrors > Home > ILE Home > Th. List > prarloclemn | Unicode version |
Description: Subtracting two from a positive integer. Lemma for prarloc 7279. (Contributed by Jim Kingdon, 5-Nov-2019.) |
Ref | Expression |
---|---|
prarloclemn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simpl 108 | . . 3 | |
2 | 1pi 7091 | . . . . 5 | |
3 | ltpiord 7095 | . . . . 5 | |
4 | 2, 3 | mpan 420 | . . . 4 |
5 | 4 | biimpa 294 | . . 3 |
6 | piord 7087 | . . . 4 | |
7 | ordsucss 4390 | . . . 4 | |
8 | 6, 7 | syl 14 | . . 3 |
9 | 1, 5, 8 | sylc 62 | . 2 |
10 | df-2o 6282 | . . . 4 | |
11 | 10 | sseq1i 3093 | . . 3 |
12 | pinn 7085 | . . . . 5 | |
13 | 2onn 6385 | . . . . . 6 | |
14 | nnawordex 6392 | . . . . . 6 | |
15 | 13, 14 | mpan 420 | . . . . 5 |
16 | 12, 15 | syl 14 | . . . 4 |
17 | 16 | adantr 274 | . . 3 |
18 | 11, 17 | syl5bbr 193 | . 2 |
19 | 9, 18 | mpbid 146 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1316 wcel 1465 wrex 2394 wss 3041 class class class wbr 3899 word 4254 csuc 4257 com 4474 (class class class)co 5742 c1o 6274 c2o 6275 coa 6278 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-in1 588 ax-in2 589 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-13 1476 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-coll 4013 ax-sep 4016 ax-nul 4024 ax-pow 4068 ax-pr 4101 ax-un 4325 ax-setind 4422 ax-iinf 4472 |
This theorem depends on definitions: df-bi 116 df-3or 948 df-3an 949 df-tru 1319 df-fal 1322 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-ne 2286 df-ral 2398 df-rex 2399 df-reu 2400 df-rab 2402 df-v 2662 df-sbc 2883 df-csb 2976 df-dif 3043 df-un 3045 df-in 3047 df-ss 3054 df-nul 3334 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-uni 3707 df-int 3742 df-iun 3785 df-br 3900 df-opab 3960 df-mpt 3961 df-tr 3997 df-eprel 4181 df-id 4185 df-iord 4258 df-on 4260 df-suc 4263 df-iom 4475 df-xp 4515 df-rel 4516 df-cnv 4517 df-co 4518 df-dm 4519 df-rn 4520 df-res 4521 df-ima 4522 df-iota 5058 df-fun 5095 df-fn 5096 df-f 5097 df-f1 5098 df-fo 5099 df-f1o 5100 df-fv 5101 df-ov 5745 df-oprab 5746 df-mpo 5747 df-1st 6006 df-2nd 6007 df-recs 6170 df-irdg 6235 df-1o 6281 df-2o 6282 df-oadd 6285 df-ni 7080 df-lti 7083 |
This theorem is referenced by: prarloclem5 7276 |
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