Theorem rexri 8077

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 8065	. 2 |- ( A e. RR -> A e. RR* )
3	1, 2	ax-mp 5	1 |- A e. RR*

Syntax hints:   e. wcel 2164   RRcr 7871   RR*cxr 8053

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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-nfc 2325  df-v 2762  df-un 3157  df-in 3159  df-ss 3166  df-xr 8058

This theorem is referenced by:  1xr  8078  cos12dec  11911  halfleoddlt  12035  reeff1oleme  14907  reeff1o  14908  sin0pilem2  14917  neghalfpirx  14929  sincosq1sgn  14961  sincosq2sgn  14962  sincosq4sgn  14964  sinq12gt0  14965  cosq14gt0  14967  cosq23lt0  14968  coseq0q4123  14969  coseq00topi  14970  coseq0negpitopi  14971  cosordlem  14984  cosq34lt1  14985  cos02pilt1  14986  cos0pilt1  14987  ioocosf1o  14989  negpitopissre  14990  iooref1o  15524  taupi  15563