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Theorem rexrd 7783
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 7777 . 2  |-  RR  C_  RR*
2 rexrd.1 . 2  |-  ( ph  ->  A  e.  RR )
31, 2sseldi 3065 1  |-  ( ph  ->  A  e.  RR* )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1465   RRcr 7587   RR*cxr 7767
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 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-xr 7772
This theorem is referenced by:  xnn0xr  9013  rpxr  9417  rpxrd  9452  xnegcl  9583  xaddf  9595  xaddval  9596  xnn0lenn0nn0  9616  xposdif  9633  iooshf  9703  icoshftf1o  9742  ioo0  10005  ioom  10006  ico0  10007  ioc0  10008  modqelico  10075  mulqaddmodid  10105  addmodid  10113  elicc4abs  10834  xrmaxiflemcl  10982  xblss2ps  12500  xblss2  12501  blss2ps  12502  blss2  12503  blhalf  12504  cnblcld  12631  ioo2blex  12640  tgioo  12642  cnopnap  12690  suplociccreex  12698  suplociccex  12699  dedekindicc  12707  ivthinclemlm  12708  ivthinclemum  12709  ivthinclemlopn  12710  ivthinclemuopn  12712  ivthdec  12718  sin0pilem2  12790  pilem3  12791
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