Theorem rexri 8215

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 8203	. 2 |- ( A e. RR -> A e. RR* )
3	1, 2	ax-mp 5	1 |- A e. RR*

Syntax hints:   e. wcel 2200   RRcr 8009   RR*cxr 8191

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-v 2801  df-un 3201  df-in 3203  df-ss 3210  df-xr 8196

This theorem is referenced by:  1xr  8216  cos12dec  12294  halfleoddlt  12420  reeff1oleme  15461  reeff1o  15462  sin0pilem2  15471  neghalfpirx  15483  sincosq1sgn  15515  sincosq2sgn  15516  sincosq4sgn  15518  sinq12gt0  15519  cosq14gt0  15521  cosq23lt0  15522  coseq0q4123  15523  coseq00topi  15524  coseq0negpitopi  15525  cosordlem  15538  cosq34lt1  15539  cos02pilt1  15540  cos0pilt1  15541  ioocosf1o  15543  negpitopissre  15544  iooref1o  16462  taupi  16501