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Theorem rexri 7791
Description: A standard real is an extended real (inference form.) (Contributed by David Moews, 28-Feb-2017.)
Hypothesis
Ref Expression
rexri.1  |-  A  e.  RR
Assertion
Ref Expression
rexri  |-  A  e. 
RR*

Proof of Theorem rexri
StepHypRef Expression
1 rexri.1 . 2  |-  A  e.  RR
2 rexr 7779 . 2  |-  ( A  e.  RR  ->  A  e.  RR* )
31, 2ax-mp 5 1  |-  A  e. 
RR*
Colors of variables: wff set class
Syntax hints:    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:  cos12dec  11401  halfleoddlt  11518  sin0pilem2  12790  neghalfpirx  12802  sincosq1sgn  12834  sincosq2sgn  12835  sincosq4sgn  12837  sinq12gt0  12838  cosq14gt0  12840  cosq23lt0  12841  coseq0q4123  12842  coseq00topi  12843  coseq0negpitopi  12844  cosordlem  12857  cosq34lt1  12858  cos02pilt1  12859  taupi  13166
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