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Mirrors > Home > ILE Home > Th. List > rpgt0 | Unicode version |
Description: A positive real is greater than zero. (Contributed by FL, 27-Dec-2007.) |
Ref | Expression |
---|---|
rpgt0 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elrp 9472 |
. 2
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2 | 1 | simprbi 273 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rab 2426 df-v 2691 df-un 3080 df-sn 3538 df-pr 3539 df-op 3541 df-br 3938 df-rp 9471 |
This theorem is referenced by: rpge0 9483 rpap0 9487 rpgecl 9499 0nrp 9506 rpgt0d 9516 addlelt 9585 rpsqrtcl 10845 rpmaxcl 11027 rpmincl 11041 xrminrpcl 11075 climconst 11091 blcntrps 12623 blcntr 12624 bdmet 12710 bdmopn 12712 reeff1o 12902 coseq00topi 12964 coseq0negpitopi 12965 |
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