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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 9345 |
. 2
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4 | 1, 2, 3 | sylanbrc 411 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 681 ax-5 1406 ax-7 1407 ax-gen 1408 ax-ie1 1452 ax-ie2 1453 ax-8 1465 ax-10 1466 ax-11 1467 ax-i12 1468 ax-bndl 1469 ax-4 1470 ax-17 1489 ax-i9 1493 ax-ial 1497 ax-i5r 1498 ax-ext 2097 |
This theorem depends on definitions: df-bi 116 df-3an 947 df-tru 1317 df-nf 1420 df-sb 1719 df-clab 2102 df-cleq 2108 df-clel 2111 df-nfc 2244 df-rab 2399 df-v 2659 df-un 3041 df-sn 3499 df-pr 3500 df-op 3502 df-br 3896 df-rp 9344 |
This theorem is referenced by: zltaddlt1le 9682 modqval 9990 ltexp2a 10238 leexp2a 10239 expnlbnd2 10310 resqrexlem1arp 10669 resqrexlemp1rp 10670 resqrexlemcalc2 10679 resqrexlemcalc3 10680 resqrexlemgt0 10684 resqrexlemglsq 10686 rpsqrtcl 10705 absrpclap 10725 rpmaxcl 10887 rpmincl 10901 xrminrpcl 10935 xrbdtri 10937 mulcn2 10973 reccn2ap 10974 climge0 10986 divcnv 11158 georeclim 11174 cvgratnnlembern 11184 cvgratnnlemsumlt 11189 cvgratnnlemfm 11190 cvgratnnlemrate 11191 cvgratnn 11192 cvgratz 11193 rpefcl 11242 efltim 11255 ef01bndlem 11314 bdmopn 12493 mulcncflem 12576 |
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