ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rexr Structured version   GIF version

Theorem rexr 6868
Description: A standard real is an extended real. (Contributed by NM, 14-Oct-2005.)
Assertion
Ref Expression
rexr (A ℝ → A *)

Proof of Theorem rexr
StepHypRef Expression
1 ressxr 6866 . 2 ℝ ⊆ ℝ*
21sseli 2935 1 (A ℝ → A *)
Colors of variables: wff set class
Syntax hints:  wi 4   wcel 1390  cr 6710  *cxr 6856
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-un 2916  df-in 2918  df-ss 2925  df-xr 6861
This theorem is referenced by:  rexri  6875  lenlt  6891  ltpnf  8472  mnflt  8474  xrltnsym  8484  xrlttr  8486  xrltso  8487  xrre  8503  xrre3  8505  xltnegi  8518  elioo4g  8573  elioc2  8575  elico2  8576  elicc2  8577  iccss  8580  iooshf  8591  iooneg  8626  icoshft  8628
  Copyright terms: Public domain W3C validator