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Mirrors > Home > ILE Home > Th. List > elrp | Unicode version |
Description: Membership in the set of positive reals. (Contributed by NM, 27-Oct-2007.) |
Ref | Expression |
---|---|
elrp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq2 3903 | . 2 | |
2 | df-rp 9410 | . 2 | |
3 | 1, 2 | elrab2 2816 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 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: elrpii 9412 nnrp 9419 rpgt0 9421 rpregt0 9423 ralrp 9431 rexrp 9432 rpaddcl 9433 rpmulcl 9434 rpdivcl 9435 rpgecl 9438 rphalflt 9439 ge0p1rp 9441 rpnegap 9442 negelrp 9443 ltsubrp 9446 ltaddrp 9447 difrp 9448 elrpd 9449 iccdil 9749 icccntr 9751 expgt0 10294 sqrtdiv 10782 mulcn2 11049 ef01bndlem 11390 |
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