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Theorem rexri 8017
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 8005 . 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 7812   RR*cxr 7993
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 2741  df-un 3135  df-in 3137  df-ss 3144  df-xr 7998
This theorem is referenced by:  1xr  8018  cos12dec  11777  halfleoddlt  11901  reeff1oleme  14232  reeff1o  14233  sin0pilem2  14242  neghalfpirx  14254  sincosq1sgn  14286  sincosq2sgn  14287  sincosq4sgn  14289  sinq12gt0  14290  cosq14gt0  14292  cosq23lt0  14293  coseq0q4123  14294  coseq00topi  14295  coseq0negpitopi  14296  cosordlem  14309  cosq34lt1  14310  cos02pilt1  14311  cos0pilt1  14312  ioocosf1o  14314  negpitopissre  14315  iooref1o  14821  taupi  14859
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