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Theorem 0xr 7227
 Description: Zero is an extended real. (Contributed by Mario Carneiro, 15-Jun-2014.)
Assertion
Ref Expression
0xr 0 ∈ ℝ*

Proof of Theorem 0xr
StepHypRef Expression
1 ressxr 7224 . 2 ℝ ⊆ ℝ*
2 0re 7181 . 2 0 ∈ ℝ
31, 2sselii 2997 1 0 ∈ ℝ*
 Colors of variables: wff set class Syntax hints:   ∈ wcel 1434  ℝcr 7042  0cc0 7043  ℝ*cxr 7214 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 2064  ax-1re 7132  ax-addrcl 7135  ax-rnegex 7147 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-xr 7219 This theorem is referenced by:  0lepnf  8941  ge0gtmnf  8966  xlt0neg1  8981  xlt0neg2  8982  xle0neg1  8983  xle0neg2  8984  ioopos  9049  elxrge0  9077  0e0iccpnf  9079  halfleoddlt  10438
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