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Theorem rexri 8011
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 7999 . 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 2148   RRcr 7807   RR*cxr 7987
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-xr 7992
This theorem is referenced by:  1xr  8012  cos12dec  11768  halfleoddlt  11891  reeff1oleme  14064  reeff1o  14065  sin0pilem2  14074  neghalfpirx  14086  sincosq1sgn  14118  sincosq2sgn  14119  sincosq4sgn  14121  sinq12gt0  14122  cosq14gt0  14124  cosq23lt0  14125  coseq0q4123  14126  coseq00topi  14127  coseq0negpitopi  14128  cosordlem  14141  cosq34lt1  14142  cos02pilt1  14143  cos0pilt1  14144  ioocosf1o  14146  negpitopissre  14147  iooref1o  14642  taupi  14680
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