ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  0xr Unicode version

Theorem 0xr 7297
Description: Zero is an extended real. (Contributed by Mario Carneiro, 15-Jun-2014.)
Assertion
Ref Expression
0xr  |-  0  e.  RR*

Proof of Theorem 0xr
StepHypRef Expression
1 ressxr 7294 . 2  |-  RR  C_  RR*
2 0re 7251 . 2  |-  0  e.  RR
31, 2sselii 3005 1  |-  0  e.  RR*
Colors of variables: wff set class
Syntax hints:    e. wcel 1434   RRcr 7112   0cc0 7113   RR*cxr 7284
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-1re 7202  ax-addrcl 7205  ax-rnegex 7217
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-xr 7289
This theorem is referenced by:  0lepnf  9011  ge0gtmnf  9036  xlt0neg1  9051  xlt0neg2  9052  xle0neg1  9053  xle0neg2  9054  ioopos  9119  elxrge0  9147  0e0iccpnf  9149  halfleoddlt  10519
  Copyright terms: Public domain W3C validator