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Theorem 0xr 7471
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 7468 . 2  |-  RR  C_  RR*
2 0re 7425 . 2  |-  0  e.  RR
31, 2sselii 3011 1  |-  0  e.  RR*
Colors of variables: wff set class
Syntax hints:    e. wcel 1436   RRcr 7286   0cc0 7287   RR*cxr 7458
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 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-1re 7376  ax-addrcl 7379  ax-rnegex 7391
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360  df-rex 2361  df-v 2617  df-un 2992  df-in 2994  df-ss 3001  df-xr 7463
This theorem is referenced by:  0lepnf  9185  ge0gtmnf  9210  xlt0neg1  9225  xlt0neg2  9226  xle0neg1  9227  xle0neg2  9228  ioopos  9293  elxrge0  9321  0e0iccpnf  9323  halfleoddlt  10761
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