Theorem rexri 8129

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 8117	. 2 |- ( A e. RR -> A e. RR* )
3	1, 2	ax-mp 5	1 |- A e. RR*

Syntax hints:   e. wcel 2175   RRcr 7923   RR*cxr 8105

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 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-v 2773  df-un 3169  df-in 3171  df-ss 3178  df-xr 8110

This theorem is referenced by:  1xr  8130  cos12dec  12050  halfleoddlt  12176  reeff1oleme  15215  reeff1o  15216  sin0pilem2  15225  neghalfpirx  15237  sincosq1sgn  15269  sincosq2sgn  15270  sincosq4sgn  15272  sinq12gt0  15273  cosq14gt0  15275  cosq23lt0  15276  coseq0q4123  15277  coseq00topi  15278  coseq0negpitopi  15279  cosordlem  15292  cosq34lt1  15293  cos02pilt1  15294  cos0pilt1  15295  ioocosf1o  15297  negpitopissre  15298  iooref1o  15935  taupi  15974