ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rpgt0 Unicode version

Theorem rpgt0 8594
Description: A positive real is greater than zero. (Contributed by FL, 27-Dec-2007.)
Assertion
Ref Expression
rpgt0  |-  ( A  e.  RR+  ->  0  < 
A )

Proof of Theorem rpgt0
StepHypRef Expression
1 elrp 8585 . 2  |-  ( A  e.  RR+  <->  ( A  e.  RR  /\  0  < 
A ) )
21simprbi 260 1  |-  ( A  e.  RR+  ->  0  < 
A )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1393   class class class wbr 3764   RRcr 6888   0cc0 6889    < clt 7060   RR+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:  rpge0  8595  rpap0  8599  rpgecl  8611  0nrp  8616  rpgt0d  8625  rpsqrtcl  9639  climconst  9811
  Copyright terms: Public domain W3C validator