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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 |
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elrpd.2 |
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Ref | Expression |
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elrpd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elrpd.1 |
. 2
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2 | elrpd.2 |
. 2
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3 | elrp 9126 |
. 2
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4 | 1, 2, 3 | sylanbrc 408 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 665 ax-5 1381 ax-7 1382 ax-gen 1383 ax-ie1 1427 ax-ie2 1428 ax-8 1440 ax-10 1441 ax-11 1442 ax-i12 1443 ax-bndl 1444 ax-4 1445 ax-17 1464 ax-i9 1468 ax-ial 1472 ax-i5r 1473 ax-ext 2070 |
This theorem depends on definitions: df-bi 115 df-3an 926 df-tru 1292 df-nf 1395 df-sb 1693 df-clab 2075 df-cleq 2081 df-clel 2084 df-nfc 2217 df-rab 2368 df-v 2621 df-un 3003 df-sn 3450 df-pr 3451 df-op 3453 df-br 3844 df-rp 9125 |
This theorem is referenced by: zltaddlt1le 9413 modqval 9719 ltexp2a 9995 leexp2a 9996 expnlbnd2 10067 resqrexlem1arp 10426 resqrexlemp1rp 10427 resqrexlemcalc2 10436 resqrexlemcalc3 10437 resqrexlemgt0 10441 resqrexlemglsq 10443 rpsqrtcl 10462 absrpclap 10482 mulcn2 10688 climge0 10700 divcnv 10878 georeclim 10894 cvgratnnlembern 10904 cvgratnnlemsumlt 10909 cvgratnnlemfm 10910 cvgratnnlemrate 10911 cvgratnn 10912 cvgratz 10913 rpefcl 10962 efltim 10975 ef01bndlem 11034 |
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