Theorem rexri 8331

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 8319	. 2 |- ( A e. RR -> A e. RR* )
3	1, 2	ax-mp 5	1 |- A e. RR*

Syntax hints:   e. wcel 2203   RRcr 8126   RR*cxr 8307

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-v 2815  df-un 3215  df-in 3217  df-ss 3224  df-xr 8312

This theorem is referenced by:  1xr  8332  cos12dec  12454  halfleoddlt  12580  reeff1oleme  15637  reeff1o  15638  sin0pilem2  15647  neghalfpirx  15659  sincosq1sgn  15691  sincosq2sgn  15692  sincosq4sgn  15694  sinq12gt0  15695  cosq14gt0  15697  cosq23lt0  15698  coseq0q4123  15699  coseq00topi  15700  coseq0negpitopi  15701  cosordlem  15714  cosq34lt1  15715  cos02pilt1  15716  cos0pilt1  15717  ioocosf1o  15719  negpitopissre  15720  iooref1o  16818  taupi  16859