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Theorem prn0 7132
Description: A positive real is not empty. (Revised by Mario Carneiro, 11-May-2013.)
Assertion
Ref Expression
prn0

Proof of Theorem prn0
StepHypRef Expression
1 elnpi 7131 . . 3
2 simpl2 921 . . 3
31, 2sylbi 185 . 2
4 0pss 2944 . 2
53, 4sylib 186 1
Colors of variables: wff set class
Syntax hints:   wi 4   wa 357   w3a 899  wal 1330   wcel 1416   wne 2035  wral 2127  wrex 2128  cvv 2327   wpss 2638  c0 2907   class class class wbr 3396  cnq 6992   cltq 6998  cnp 6999
This theorem is referenced by:  0npr 7135  npomex 7139  genpn0 7146  prlem934 7176  ltaddpr 7177  prlem936 7190  reclem2pr 7191  suplem1pr 7195
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1331  ax-6 1332  ax-7 1333  ax-gen 1334  ax-8 1418  ax-10 1419  ax-11 1420  ax-12 1421  ax-17 1430  ax-9 1445  ax-4 1451  ax-16 1629  ax-ext 1900
This theorem depends on definitions:  df-bi 175  df-or 358  df-an 359  df-3an 901  df-ex 1336  df-sb 1591  df-clab 1906  df-cleq 1911  df-clel 1914  df-ne 2037  df-ral 2131  df-rex 2132  df-v 2329  df-dif 2640  df-in 2644  df-ss 2648  df-pss 2650  df-nul 2908  df-np 7124
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