Theorem rexri 8373

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 8361	. 2 |- ( A e. RR -> A e. RR* )
3	1, 2	ax-mp 5	1 |- A e. RR*

Syntax hints:   e. wcel 2209   RRcr 8168   RR*cxr 8349

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 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-v 2823  df-un 3224  df-in 3226  df-ss 3233  df-xr 8354

This theorem is referenced by:  1xr  8374  cos12dec  12513  halfleoddlt  12639  reeff1oleme  15796  reeff1o  15797  sin0pilem2  15806  neghalfpirx  15818  sincosq1sgn  15850  sincosq2sgn  15851  sincosq4sgn  15853  sinq12gt0  15854  cosq14gt0  15856  cosq23lt0  15857  coseq0q4123  15858  coseq00topi  15859  coseq0negpitopi  15860  cosordlem  15873  cosq34lt1  15874  cos02pilt1  15875  cos0pilt1  15876  ioocosf1o  15878  negpitopissre  15879  iooref1o  16988  taupi  17028