Theorem rexri 8279

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 8267	. 2 |- ( A e. RR -> A e. RR* )
3	1, 2	ax-mp 5	1 |- A e. RR*

Syntax hints:   e. wcel 2202   RRcr 8074   RR*cxr 8255

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2364  df-v 2805  df-un 3205  df-in 3207  df-ss 3214  df-xr 8260

This theorem is referenced by:  1xr  8280  cos12dec  12392  halfleoddlt  12518  reeff1oleme  15566  reeff1o  15567  sin0pilem2  15576  neghalfpirx  15588  sincosq1sgn  15620  sincosq2sgn  15621  sincosq4sgn  15623  sinq12gt0  15624  cosq14gt0  15626  cosq23lt0  15627  coseq0q4123  15628  coseq00topi  15629  coseq0negpitopi  15630  cosordlem  15643  cosq34lt1  15644  cos02pilt1  15645  cos0pilt1  15646  ioocosf1o  15648  negpitopissre  15649  iooref1o  16749  taupi  16789