Theorem rexri 8383

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 8371	. 2 |- ( A e. RR -> A e. RR* )
3	1, 2	ax-mp 5	1 |- A e. RR*

This proof depends on syntax axioms:   e. wcel 2209   RRcr 8178   RR*cxr 8359

This proof depends on 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 proof 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 8364

This theorem is used by:  1xr  8384  cos12dec  12551  halfleoddlt  12677  reeff1oleme  15922  reeff1o  15923  sin0pilem2  15933  neghalfpirx  15945  sincosq1sgn  15977  sincosq2sgn  15978  sincosq4sgn  15980  sinq12gt0  15981  cosq14gt0  15983  cosq23lt0  15984  coseq0q4123  15985  coseq00topi  15986  coseq0negpitopi  15987  cosordlem  16000  cosq34lt1  16001  cos02pilt1  16002  cos0pilt1  16003  ioocosf1o  16005  negpitopissre  16006  iooref1o  17181  taupi  17221