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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-i1p 7089 |
. 2
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2 | 1nq 6988 |
. . 3
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3 | nqprlu 7169 |
. . 3
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4 | 2, 3 | ax-mp 7 |
. 2
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5 | 1, 4 | eqeltri 2161 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 580 ax-in2 581 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-13 1450 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-coll 3962 ax-sep 3965 ax-nul 3973 ax-pow 4017 ax-pr 4047 ax-un 4271 ax-setind 4368 ax-iinf 4418 |
This theorem depends on definitions: df-bi 116 df-dc 782 df-3or 926 df-3an 927 df-tru 1293 df-fal 1296 df-nf 1396 df-sb 1694 df-eu 1952 df-mo 1953 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-ne 2257 df-ral 2365 df-rex 2366 df-reu 2367 df-rab 2369 df-v 2624 df-sbc 2844 df-csb 2937 df-dif 3004 df-un 3006 df-in 3008 df-ss 3015 df-nul 3290 df-pw 3437 df-sn 3458 df-pr 3459 df-op 3461 df-uni 3662 df-int 3697 df-iun 3740 df-br 3854 df-opab 3908 df-mpt 3909 df-tr 3945 df-eprel 4127 df-id 4131 df-po 4134 df-iso 4135 df-iord 4204 df-on 4206 df-suc 4209 df-iom 4421 df-xp 4460 df-rel 4461 df-cnv 4462 df-co 4463 df-dm 4464 df-rn 4465 df-res 4466 df-ima 4467 df-iota 4995 df-fun 5032 df-fn 5033 df-f 5034 df-f1 5035 df-fo 5036 df-f1o 5037 df-fv 5038 df-ov 5671 df-oprab 5672 df-mpt2 5673 df-1st 5927 df-2nd 5928 df-recs 6086 df-irdg 6151 df-1o 6197 df-oadd 6201 df-omul 6202 df-er 6308 df-ec 6310 df-qs 6314 df-ni 6926 df-pli 6927 df-mi 6928 df-lti 6929 df-plpq 6966 df-mpq 6967 df-enq 6969 df-nqqs 6970 df-plqqs 6971 df-mqqs 6972 df-1nqqs 6973 df-rq 6974 df-ltnqqs 6975 df-inp 7088 df-i1p 7089 |
This theorem is referenced by: 1idprl 7212 1idpru 7213 1idpr 7214 recexprlemex 7259 ltmprr 7264 gt0srpr 7357 0r 7359 1sr 7360 m1r 7361 m1p1sr 7369 m1m1sr 7370 0lt1sr 7374 0idsr 7376 1idsr 7377 00sr 7378 recexgt0sr 7382 archsr 7390 srpospr 7391 prsrcl 7392 prsrpos 7393 prsradd 7394 prsrlt 7395 caucvgsrlembound 7402 pitonnlem1p1 7446 pitonnlem2 7447 pitonn 7448 pitoregt0 7449 pitore 7450 recnnre 7451 recidpirqlemcalc 7457 recidpirq 7458 |
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