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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 9399 | . 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 9397 |
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 9398 |
This theorem is referenced by: mul2lt0rgt0 9502 mul2lt0np 9505 zltaddlt1le 9744 modqval 10052 ltexp2a 10300 leexp2a 10301 expnlbnd2 10372 resqrexlem1arp 10732 resqrexlemp1rp 10733 resqrexlemcalc2 10742 resqrexlemcalc3 10743 resqrexlemgt0 10747 resqrexlemglsq 10749 rpsqrtcl 10768 absrpclap 10788 rpmaxcl 10950 rpmincl 10964 xrminrpcl 10998 xrbdtri 11000 mulcn2 11036 reccn2ap 11037 climge0 11049 divcnv 11221 georeclim 11237 cvgratnnlembern 11247 cvgratnnlemsumlt 11252 cvgratnnlemfm 11253 cvgratnnlemrate 11254 cvgratnn 11255 cvgratz 11256 rpefcl 11305 efltim 11318 ef01bndlem 11377 bdmopn 12584 mulcncflem 12670 ivthinclemlopn 12694 ivthinclemuopn 12696 dveflem 12766 pilem3 12775 |
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