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Theorem rexri 8014
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 8002 . 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 7809   RR*cxr 7990
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 7995
This theorem is referenced by:  1xr  8015  cos12dec  11774  halfleoddlt  11898  reeff1oleme  14163  reeff1o  14164  sin0pilem2  14173  neghalfpirx  14185  sincosq1sgn  14217  sincosq2sgn  14218  sincosq4sgn  14220  sinq12gt0  14221  cosq14gt0  14223  cosq23lt0  14224  coseq0q4123  14225  coseq00topi  14226  coseq0negpitopi  14227  cosordlem  14240  cosq34lt1  14241  cos02pilt1  14242  cos0pilt1  14243  ioocosf1o  14245  negpitopissre  14246  iooref1o  14752  taupi  14790
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