Theorem rexri 8130

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

Step	Hyp	Ref	Expression
1		rexri.1	. 2 |- A e. RR
2		rexr 8118	. 2 |- ( A e. RR -> A e. RR* )
3	1, 2	ax-mp 5	1 |- A e. RR*

Syntax hints:   e. wcel 2176   RRcr 7924   RR*cxr 8106

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-v 2774  df-un 3170  df-in 3172  df-ss 3179  df-xr 8111

This theorem is referenced by:  1xr  8131  cos12dec  12079  halfleoddlt  12205  reeff1oleme  15244  reeff1o  15245  sin0pilem2  15254  neghalfpirx  15266  sincosq1sgn  15298  sincosq2sgn  15299  sincosq4sgn  15301  sinq12gt0  15302  cosq14gt0  15304  cosq23lt0  15305  coseq0q4123  15306  coseq00topi  15307  coseq0negpitopi  15308  cosordlem  15321  cosq34lt1  15322  cos02pilt1  15323  cos0pilt1  15324  ioocosf1o  15326  negpitopissre  15327  iooref1o  15973  taupi  16012