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  12535  halfleoddlt  12661  reeff1oleme  15873  reeff1o  15874  sin0pilem2  15883  neghalfpirx  15895  sincosq1sgn  15927  sincosq2sgn  15928  sincosq4sgn  15930  sinq12gt0  15931  cosq14gt0  15933  cosq23lt0  15934  coseq0q4123  15935  coseq00topi  15936  coseq0negpitopi  15937  cosordlem  15950  cosq34lt1  15951  cos02pilt1  15952  cos0pilt1  15953  ioocosf1o  15955  negpitopissre  15956  iooref1o  17083  taupi  17123