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Theorem rpred 8397
Description: A positive real is a real. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
rpred.1  RR+
Assertion
Ref Expression
rpred  RR

Proof of Theorem rpred
StepHypRef Expression
1 rpssre 8368 . 2  RR+  C_  RR
2 rpred.1 . 2  RR+
31, 2sseldi 2937 1  RR
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1390   RRcr 6710   RR+crp 8358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rab 2309  df-in 2918  df-ss 2925  df-rp 8359
This theorem is referenced by:  rpxrd  8398  rpcnd  8399  rpregt0d  8403  rprege0d  8404  rprene0d  8405  rprecred  8408  ltmulgt11d  8428  ltmulgt12d  8429  gt0divd  8430  ge0divd  8431  lediv12ad  8452  ltexp2a  8960  leexp2a  8961  expnlbnd2  9027
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