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Theorem rpgt0d 9085
Description: A positive real is greater than zero. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
rpred.1  |-  ( ph  ->  A  e.  RR+ )
Assertion
Ref Expression
rpgt0d  |-  ( ph  ->  0  <  A )

Proof of Theorem rpgt0d
StepHypRef Expression
1 rpred.1 . 2  |-  ( ph  ->  A  e.  RR+ )
2 rpgt0 9054 . 2  |-  ( A  e.  RR+  ->  0  < 
A )
31, 2syl 14 1  |-  ( ph  ->  0  <  A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1436   class class class wbr 3814   0cc0 7271    < clt 7443   RR+crp 9043
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 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-3an 924  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-rab 2364  df-v 2616  df-un 2990  df-sn 3431  df-pr 3432  df-op 3434  df-br 3815  df-rp 9044
This theorem is referenced by:  rpregt0d  9089  ltmulgt11d  9118  ltmulgt12d  9119  gt0divd  9120  ge0divd  9121  lediv12ad  9142  expgt0  9839  nnesq  9922  bccl2  10025  resqrexlemp1rp  10280  resqrexlemover  10284  resqrexlemnm  10292  resqrexlemgt0  10294  resqrexlemglsq  10296  sqrtgt0d  10433  prmind2  10896  sqrt2irrlem  10934
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