Theorem rexri 8227

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 8215	. 2 |- ( A e. RR -> A e. RR* )
3	1, 2	ax-mp 5	1 |- A e. RR*

Syntax hints:   e. wcel 2200   RRcr 8021   RR*cxr 8203

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 2802  df-un 3202  df-in 3204  df-ss 3211  df-xr 8208

This theorem is referenced by:  1xr  8228  cos12dec  12319  halfleoddlt  12445  reeff1oleme  15486  reeff1o  15487  sin0pilem2  15496  neghalfpirx  15508  sincosq1sgn  15540  sincosq2sgn  15541  sincosq4sgn  15543  sinq12gt0  15544  cosq14gt0  15546  cosq23lt0  15547  coseq0q4123  15548  coseq00topi  15549  coseq0negpitopi  15550  cosordlem  15563  cosq34lt1  15564  cos02pilt1  15565  cos0pilt1  15566  ioocosf1o  15568  negpitopissre  15569  iooref1o  16574  taupi  16613