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Theorem rexri 7835
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 7823 . 2 (𝐴 ∈ ℝ → 𝐴 ∈ ℝ*)
31, 2ax-mp 5 1 𝐴 ∈ ℝ*
Colors of variables: wff set class
Syntax hints:  wcel 1480  cr 7631  *cxr 7811
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 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-xr 7816
This theorem is referenced by:  cos12dec  11485  halfleoddlt  11602  reeff1oleme  12876  reeff1o  12877  sin0pilem2  12885  neghalfpirx  12897  sincosq1sgn  12929  sincosq2sgn  12930  sincosq4sgn  12932  sinq12gt0  12933  cosq14gt0  12935  cosq23lt0  12936  coseq0q4123  12937  coseq00topi  12938  coseq0negpitopi  12939  cosordlem  12952  cosq34lt1  12953  cos02pilt1  12954  cos0pilt1  12955  ioocosf1o  12957  negpitopissre  12958  taupi  13351
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