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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rp 9684 |
. . 3
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2 | ssrab2 3255 |
. . 3
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3 | 1, 2 | eqsstri 3202 |
. 2
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4 | 3 | sseli 3166 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-ext 2171 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rab 2477 df-in 3150 df-ss 3157 df-rp 9684 |
This theorem is referenced by: rpxr 9691 rpcn 9692 rpssre 9694 rpge0 9696 rprege0 9698 rpap0 9700 rprene0 9701 rpreap0 9702 rpaddcl 9707 rpmulcl 9708 rpdivcl 9709 rpgecl 9712 ledivge1le 9756 addlelt 9798 iccdil 10028 expnlbnd 10676 caucvgre 11022 rennim 11043 rpsqrtcl 11082 qdenre 11243 rpmaxcl 11264 rpmincl 11278 xrminrpcl 11314 2clim 11341 cn1lem 11354 climsqz 11375 climsqz2 11376 climcau 11387 efgt1 11737 ef01bndlem 11796 bdmet 14459 bdmopn 14461 dveflem 14644 reeff1o 14651 logleb 14753 logrpap0b 14754 cxple3 14798 rpcxpsqrt 14799 rpcxpsqrtth 14807 dceqnconst 15267 dcapnconst 15268 |
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