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Mirrors > Home > ILE Home > Th. List > elrpd | Unicode version |
Description: Membership in the set of positive reals. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
elrpd.1 | |
elrpd.2 |
Ref | Expression |
---|---|
elrpd |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elrpd.1 | . 2 | |
2 | elrpd.2 | . 2 | |
3 | elrp 9411 | . 2 | |
4 | 1, 2, 3 | sylanbrc 413 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1465 class class class wbr 3899 cr 7587 cc0 7588 clt 7768 crp 9409 |
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-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-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-rab 2402 df-v 2662 df-un 3045 df-sn 3503 df-pr 3504 df-op 3506 df-br 3900 df-rp 9410 |
This theorem is referenced by: mul2lt0rgt0 9515 mul2lt0np 9518 zltaddlt1le 9757 modqval 10065 ltexp2a 10313 leexp2a 10314 expnlbnd2 10385 resqrexlem1arp 10745 resqrexlemp1rp 10746 resqrexlemcalc2 10755 resqrexlemcalc3 10756 resqrexlemgt0 10760 resqrexlemglsq 10762 rpsqrtcl 10781 absrpclap 10801 rpmaxcl 10963 rpmincl 10977 xrminrpcl 11011 xrbdtri 11013 mulcn2 11049 reccn2ap 11050 climge0 11062 divcnv 11234 georeclim 11250 cvgratnnlembern 11260 cvgratnnlemsumlt 11265 cvgratnnlemfm 11266 cvgratnnlemrate 11267 cvgratnn 11268 cvgratz 11269 rpefcl 11318 efltim 11331 ef01bndlem 11390 bdmopn 12600 mulcncflem 12686 ivthinclemlopn 12710 ivthinclemuopn 12712 dveflem 12782 pilem3 12791 tanrpcl 12845 cosordlem 12857 |
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