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Theorem prn0 7045
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 7044 . . 3
2 simpl2 921 . . 3
31, 2sylbi 185 . 2
4 0pss 2939 . 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 2324   wpss 2635  c0 2902   class class class wbr 3370  cnq 6905   cltq 6911  cnp 6912
This theorem is referenced by:  0npr 7048  npomex 7052  genpn0 7059  prlem934 7089  ltaddpr 7090  prlem936 7103  reclem2pr 7104  suplem1pr 7108
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 2326  df-dif 2637  df-in 2641  df-ss 2645  df-pss 2647  df-nul 2903  df-np 7037
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