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Mirrors > Home > ILE Home > Th. List > rpcnd | Unicode version |
Description: A positive real is a complex number. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
rpred.1 |
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Ref | Expression |
---|---|
rpcnd |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpred.1 |
. . 3
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2 | 1 | rpred 9699 |
. 2
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3 | 2 | recnd 7989 |
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 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-resscn 7906 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-rab 2464 df-in 3137 df-ss 3144 df-rp 9657 |
This theorem is referenced by: rpcnne0d 9709 ltaddrp2d 9734 iccf1o 10007 bcp1nk 10745 bcpasc 10749 cvg1nlemcxze 10994 cvg1nlemres 10997 resqrexlemdec 11023 resqrexlemlo 11025 resqrexlemcalc2 11027 resqrexlemcalc3 11028 resqrexlemnm 11030 resqrexlemcvg 11031 resqrexlemoverl 11033 sqrtdiv 11054 absdivap 11082 bdtrilem 11250 isumrpcl 11505 expcnvap0 11513 absgtap 11521 cvgratz 11543 mertenslemi1 11546 effsumlt 11703 pythagtriplem12 12278 pythagtriplem14 12280 pythagtriplem16 12282 limcimolemlt 14273 rpdivcxp 14472 rpcxple2 14478 rpcxplt2 14479 rpcxpsqrt 14482 rpabscxpbnd 14499 logbgcd1irr 14525 iooref1o 14923 trilpolemclim 14925 trilpolemisumle 14927 trilpolemeq1 14929 trilpolemlt1 14930 |
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