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Theorem rexr 7226
Description: A standard real is an extended real. (Contributed by NM, 14-Oct-2005.)
Assertion
Ref Expression
rexr  |-  ( A  e.  RR  ->  A  e.  RR* )

Proof of Theorem rexr
StepHypRef Expression
1 ressxr 7224 . 2  |-  RR  C_  RR*
21sseli 2996 1  |-  ( A  e.  RR  ->  A  e.  RR* )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1434   RRcr 7042   RR*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
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-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-xr 7219
This theorem is referenced by:  rexri  7238  lenlt  7254  ltpnf  8932  mnflt  8934  xrltnsym  8944  xrlttr  8946  xrltso  8947  xrre  8963  xrre3  8965  xltnegi  8978  elioo4g  9033  elioc2  9035  elico2  9036  elicc2  9037  iccss  9040  iooshf  9051  iooneg  9086  icoshft  9088  qbtwnxr  9344  modqmuladdim  9449  elicc4abs  10118  icodiamlt  10204
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