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Theorem rexri 7816
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 7804 . 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 1480   RRcr 7612   RR*cxr 7792
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 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-xr 7797
This theorem is referenced by:  cos12dec  11463  halfleoddlt  11580  sin0pilem2  12852  neghalfpirx  12864  sincosq1sgn  12896  sincosq2sgn  12897  sincosq4sgn  12899  sinq12gt0  12900  cosq14gt0  12902  cosq23lt0  12903  coseq0q4123  12904  coseq00topi  12905  coseq0negpitopi  12906  cosordlem  12919  cosq34lt1  12920  cos02pilt1  12921  taupi  13228
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