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Theorem ressxr 7529
Description: The standard reals are a subset of the extended reals. (Contributed by NM, 14-Oct-2005.)
Assertion
Ref Expression
ressxr ℝ ⊆ ℝ*

Proof of Theorem ressxr
StepHypRef Expression
1 ssun1 3163 . 2 ℝ ⊆ (ℝ ∪ {+∞, -∞})
2 df-xr 7524 . 2 * = (ℝ ∪ {+∞, -∞})
31, 2sseqtr4i 3059 1 ℝ ⊆ ℝ*
Colors of variables: wff set class
Syntax hints:  cun 2997  wss 2999  {cpr 3447  cr 7347  +∞cpnf 7517  -∞cmnf 7518  *cxr 7519
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3003  df-in 3005  df-ss 3012  df-xr 7524
This theorem is referenced by:  rexpssxrxp  7530  rexr  7531  0xr  7532  rexrd  7535  ltrelxr  7545  iooval2  9331  fzval2  9425  iseqcoll  10243  isummolem2a  10767
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