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Mirrors > Home > ILE Home > Th. List > 1pr | Unicode version |
Description: The positive real number 'one'. (Contributed by NM, 13-Mar-1996.) (Revised by Mario Carneiro, 12-Jun-2013.) |
Ref | Expression |
---|---|
1pr |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-i1p 6565 | . 2 | |
2 | 1nq 6464 | . . 3 | |
3 | nqprlu 6645 | . . 3 | |
4 | 2, 3 | ax-mp 7 | . 2 |
5 | 1, 4 | eqeltri 2110 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1393 cab 2026 cop 3378 class class class wbr 3764 cnq 6378 c1q 6379 cltq 6383 cnp 6389 c1p 6390 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-coll 3872 ax-sep 3875 ax-nul 3883 ax-pow 3927 ax-pr 3944 ax-un 4170 ax-setind 4262 ax-iinf 4311 |
This theorem depends on definitions: df-bi 110 df-dc 743 df-3or 886 df-3an 887 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-eu 1903 df-mo 1904 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-ne 2206 df-ral 2311 df-rex 2312 df-reu 2313 df-rab 2315 df-v 2559 df-sbc 2765 df-csb 2853 df-dif 2920 df-un 2922 df-in 2924 df-ss 2931 df-nul 3225 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-int 3616 df-iun 3659 df-br 3765 df-opab 3819 df-mpt 3820 df-tr 3855 df-eprel 4026 df-id 4030 df-po 4033 df-iso 4034 df-iord 4103 df-on 4105 df-suc 4108 df-iom 4314 df-xp 4351 df-rel 4352 df-cnv 4353 df-co 4354 df-dm 4355 df-rn 4356 df-res 4357 df-ima 4358 df-iota 4867 df-fun 4904 df-fn 4905 df-f 4906 df-f1 4907 df-fo 4908 df-f1o 4909 df-fv 4910 df-ov 5515 df-oprab 5516 df-mpt2 5517 df-1st 5767 df-2nd 5768 df-recs 5920 df-irdg 5957 df-1o 6001 df-oadd 6005 df-omul 6006 df-er 6106 df-ec 6108 df-qs 6112 df-ni 6402 df-pli 6403 df-mi 6404 df-lti 6405 df-plpq 6442 df-mpq 6443 df-enq 6445 df-nqqs 6446 df-plqqs 6447 df-mqqs 6448 df-1nqqs 6449 df-rq 6450 df-ltnqqs 6451 df-inp 6564 df-i1p 6565 |
This theorem is referenced by: 1idprl 6688 1idpru 6689 1idpr 6690 recexprlemex 6735 ltmprr 6740 gt0srpr 6833 0r 6835 1sr 6836 m1r 6837 m1p1sr 6845 m1m1sr 6846 0lt1sr 6850 0idsr 6852 1idsr 6853 00sr 6854 recexgt0sr 6858 archsr 6866 srpospr 6867 prsrcl 6868 prsrpos 6869 prsradd 6870 prsrlt 6871 caucvgsrlembound 6878 pitonnlem1p1 6922 pitonnlem2 6923 pitonn 6924 pitoregt0 6925 pitore 6926 recnnre 6927 recidpirqlemcalc 6933 recidpirq 6934 |
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