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Theorem rexri 7992
Description: A standard real is an extended real (inference form.) (Contributed by David Moews, 28-Feb-2017.)
Hypothesis
Ref Expression
rexri.1 𝐴 ∈ ℝ
Assertion
Ref Expression
rexri 𝐴 ∈ ℝ*

Proof of Theorem rexri
StepHypRef Expression
1 rexri.1 . 2 𝐴 ∈ ℝ
2 rexr 7980 . 2 (𝐴 ∈ ℝ → 𝐴 ∈ ℝ*)
31, 2ax-mp 5 1 𝐴 ∈ ℝ*
Colors of variables: wff set class
Syntax hints:  wcel 2148  cr 7788  *cxr 7968
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 7973
This theorem is referenced by:  1xr  7993  cos12dec  11746  halfleoddlt  11869  reeff1oleme  13826  reeff1o  13827  sin0pilem2  13836  neghalfpirx  13848  sincosq1sgn  13880  sincosq2sgn  13881  sincosq4sgn  13883  sinq12gt0  13884  cosq14gt0  13886  cosq23lt0  13887  coseq0q4123  13888  coseq00topi  13889  coseq0negpitopi  13890  cosordlem  13903  cosq34lt1  13904  cos02pilt1  13905  cos0pilt1  13906  ioocosf1o  13908  negpitopissre  13909  iooref1o  14405  taupi  14441
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