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Mirrors > Home > ILE Home > Th. List > rpre | Unicode version |
Description: A positive real is a real. (Contributed by NM, 27-Oct-2007.) |
Ref | Expression |
---|---|
rpre |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rp 8584 | . . 3 | |
2 | ssrab2 3025 | . . 3 | |
3 | 1, 2 | eqsstri 2975 | . 2 |
4 | 3 | sseli 2941 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wcel 1393 crab 2310 class class class wbr 3764 cr 6888 cc0 6889 clt 7060 crp 8583 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-rab 2315 df-in 2924 df-ss 2931 df-rp 8584 |
This theorem is referenced by: rpxr 8590 rpcn 8591 rpssre 8593 rpge0 8595 rprege0 8597 rpap0 8599 rprene0 8600 rpreap0 8601 rpaddcl 8606 rpmulcl 8607 rpdivcl 8608 rpgecl 8611 ledivge1le 8652 iccdil 8866 expnlbnd 9373 caucvgre 9580 rennim 9600 rpsqrtcl 9639 qdenre 9798 2clim 9822 cn1lem 9834 climsqz 9855 climsqz2 9856 climcau 9866 |
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