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Theorem rpgt0d 8625
 Description: A positive real is greater than zero. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
rpred.1
Assertion
Ref Expression
rpgt0d

Proof of Theorem rpgt0d
StepHypRef Expression
1 rpred.1 . 2
2 rpgt0 8594 . 2
31, 2syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wcel 1393   class class class wbr 3764  cc0 6889   clt 7060  crp 8583 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 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-rab 2315  df-v 2559  df-un 2922  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-rp 8584 This theorem is referenced by:  rpregt0d  8629  ltmulgt11d  8658  ltmulgt12d  8659  gt0divd  8660  ge0divd  8661  lediv12ad  8682  expgt0  9288  nnesq  9368  resqrexlemp1rp  9604  resqrexlemover  9608  resqrexlemnm  9616  resqrexlemgt0  9618  resqrexlemglsq  9620  sqrtgt0d  9755  sqr2irrlem  9877
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