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Mirrors > Home > ILE Home > Th. List > pitore | Unicode version |
Description: Embedding from ![]() ![]() |
Ref | Expression |
---|---|
pitore |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nnprlu 7110 |
. . . . . 6
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2 | 1pr 7111 |
. . . . . 6
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3 | addclpr 7094 |
. . . . . 6
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4 | 1, 2, 3 | sylancl 404 |
. . . . 5
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5 | opelxpi 4469 |
. . . . 5
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6 | 4, 2, 5 | sylancl 404 |
. . . 4
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7 | enrex 7281 |
. . . . 5
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8 | 7 | ecelqsi 6344 |
. . . 4
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9 | 6, 8 | syl 14 |
. . 3
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10 | df-nr 7271 |
. . 3
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11 | 9, 10 | syl6eleqr 2181 |
. 2
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12 | opelreal 7363 |
. 2
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13 | 11, 12 | sylibr 132 |
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 104 ax-ia2 105 ax-ia3 106 ax-in1 579 ax-in2 580 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-13 1449 ax-14 1450 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 ax-coll 3954 ax-sep 3957 ax-nul 3965 ax-pow 4009 ax-pr 4036 ax-un 4260 ax-setind 4353 ax-iinf 4403 |
This theorem depends on definitions: df-bi 115 df-dc 781 df-3or 925 df-3an 926 df-tru 1292 df-fal 1295 df-nf 1395 df-sb 1693 df-eu 1951 df-mo 1952 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-ne 2256 df-ral 2364 df-rex 2365 df-reu 2366 df-rab 2368 df-v 2621 df-sbc 2841 df-csb 2934 df-dif 3001 df-un 3003 df-in 3005 df-ss 3012 df-nul 3287 df-pw 3431 df-sn 3452 df-pr 3453 df-op 3455 df-uni 3654 df-int 3689 df-iun 3732 df-br 3846 df-opab 3900 df-mpt 3901 df-tr 3937 df-eprel 4116 df-id 4120 df-po 4123 df-iso 4124 df-iord 4193 df-on 4195 df-suc 4198 df-iom 4406 df-xp 4444 df-rel 4445 df-cnv 4446 df-co 4447 df-dm 4448 df-rn 4449 df-res 4450 df-ima 4451 df-iota 4980 df-fun 5017 df-fn 5018 df-f 5019 df-f1 5020 df-fo 5021 df-f1o 5022 df-fv 5023 df-ov 5655 df-oprab 5656 df-mpt2 5657 df-1st 5911 df-2nd 5912 df-recs 6070 df-irdg 6135 df-1o 6181 df-2o 6182 df-oadd 6185 df-omul 6186 df-er 6290 df-ec 6292 df-qs 6296 df-ni 6861 df-pli 6862 df-mi 6863 df-lti 6864 df-plpq 6901 df-mpq 6902 df-enq 6904 df-nqqs 6905 df-plqqs 6906 df-mqqs 6907 df-1nqqs 6908 df-rq 6909 df-ltnqqs 6910 df-enq0 6981 df-nq0 6982 df-0nq0 6983 df-plq0 6984 df-mq0 6985 df-inp 7023 df-i1p 7024 df-iplp 7025 df-enr 7270 df-nr 7271 df-0r 7275 df-r 7358 |
This theorem is referenced by: recriota 7423 |
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