Theorem rexri 8165

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 8153	. 2 |- ( A e. RR -> A e. RR* )
3	1, 2	ax-mp 5	1 |- A e. RR*

Syntax hints:   e. wcel 2178   RRcr 7959   RR*cxr 8141

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 711  ax-5 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-10 1529  ax-11 1530  ax-i12 1531  ax-bndl 1533  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-nfc 2339  df-v 2778  df-un 3178  df-in 3180  df-ss 3187  df-xr 8146

This theorem is referenced by:  1xr  8166  cos12dec  12194  halfleoddlt  12320  reeff1oleme  15359  reeff1o  15360  sin0pilem2  15369  neghalfpirx  15381  sincosq1sgn  15413  sincosq2sgn  15414  sincosq4sgn  15416  sinq12gt0  15417  cosq14gt0  15419  cosq23lt0  15420  coseq0q4123  15421  coseq00topi  15422  coseq0negpitopi  15423  cosordlem  15436  cosq34lt1  15437  cos02pilt1  15438  cos0pilt1  15439  ioocosf1o  15441  negpitopissre  15442  iooref1o  16175  taupi  16214