Theorem rexrd 7168

Description: A standard real is an extended real. (Contributed by Mario Carneiro, 28-May-2016.)

Hypothesis

Ref	Expression
rexrd.1	|- ( ph -> A e. RR )

Assertion

Ref	Expression
rexrd	|- ( ph -> A e. RR* )

Proof of Theorem rexrd

Step	Hyp	Ref	Expression
1		ressxr 7162	. 2 |- RR C_ RR*
2		rexrd.1	. 2 |- ( ph -> A e. RR )
3	1, 2	sseldi 2997	1 |- ( ph -> A e. RR* )

Syntax hints:   -> wi 4   e. wcel 1433   RRcr 6980   RR*cxr 7152

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662  ax-5 1376  ax-7 1377  ax-gen 1378  ax-ie1 1422  ax-ie2 1423  ax-8 1435  ax-10 1436  ax-11 1437  ax-i12 1438  ax-bndl 1439  ax-4 1440  ax-17 1459  ax-i9 1463  ax-ial 1467  ax-i5r 1468  ax-ext 2063

This theorem depends on definitions:  df-bi 115  df-tru 1287  df-nf 1390  df-sb 1686  df-clab 2068  df-cleq 2074  df-clel 2077  df-nfc 2208  df-v 2603  df-un 2977  df-in 2979  df-ss 2986  df-xr 7157

This theorem is referenced by:  rpxr  8741  rpxrd  8774  xnegcl  8899  iooshf  8975  icoshftf1o  9013  ioo0  9268  ioom  9269  ico0  9270  ioc0  9271  modqelico  9336  mulqaddmodid  9366  addmodid  9374  elicc4abs  9980