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Theorem rexrd 7822
Description: A standard real is an extended real. (Contributed by Mario Carneiro, 28-May-2016.)
Hypothesis
Ref Expression
rexrd.1  |-  ( ph  ->  A  e.  RR )
Assertion
Ref Expression
rexrd  |-  ( ph  ->  A  e.  RR* )

Proof of Theorem rexrd
StepHypRef Expression
1 ressxr 7816 . 2  |-  RR  C_  RR*
2 rexrd.1 . 2  |-  ( ph  ->  A  e.  RR )
31, 2sseldi 3095 1  |-  ( ph  ->  A  e.  RR* )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1480   RRcr 7626   RR*cxr 7806
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-xr 7811
This theorem is referenced by:  xnn0xr  9052  rpxr  9456  rpxrd  9491  xnegcl  9622  xaddf  9634  xaddval  9635  xnn0lenn0nn0  9655  xposdif  9672  iooshf  9742  icoshftf1o  9781  ioo0  10044  ioom  10045  ico0  10046  ioc0  10047  modqelico  10114  mulqaddmodid  10144  addmodid  10152  elicc4abs  10873  xrmaxiflemcl  11021  xblss2ps  12583  xblss2  12584  blss2ps  12585  blss2  12586  blhalf  12587  cnblcld  12714  ioo2blex  12723  tgioo  12725  cnopnap  12773  suplociccreex  12781  suplociccex  12782  dedekindicc  12790  ivthinclemlm  12791  ivthinclemum  12792  ivthinclemlopn  12793  ivthinclemuopn  12795  ivthdec  12801  sin0pilem2  12876  pilem3  12877
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