Theorem rexri 8200

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 8188	. 2 |- ( A e. RR -> A e. RR* )
3	1, 2	ax-mp 5	1 |- A e. RR*

Syntax hints:   e. wcel 2200   RRcr 7994   RR*cxr 8176

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 8181

This theorem is referenced by:  1xr  8201  cos12dec  12274  halfleoddlt  12400  reeff1oleme  15440  reeff1o  15441  sin0pilem2  15450  neghalfpirx  15462  sincosq1sgn  15494  sincosq2sgn  15495  sincosq4sgn  15497  sinq12gt0  15498  cosq14gt0  15500  cosq23lt0  15501  coseq0q4123  15502  coseq00topi  15503  coseq0negpitopi  15504  cosordlem  15517  cosq34lt1  15518  cos02pilt1  15519  cos0pilt1  15520  ioocosf1o  15522  negpitopissre  15523  iooref1o  16361  taupi  16400