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Theorem ressxr 7853
 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 3245 . 2 ℝ ⊆ (ℝ ∪ {+∞, -∞})
2 df-xr 7848 . 2 * = (ℝ ∪ {+∞, -∞})
31, 2sseqtrri 3138 1 ℝ ⊆ ℝ*
 Colors of variables: wff set class Syntax hints:   ∪ cun 3075   ⊆ wss 3077  {cpr 3534  ℝcr 7663  +∞cpnf 7841  -∞cmnf 7842  ℝ*cxr 7843 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-un 3081  df-in 3083  df-ss 3090  df-xr 7848 This theorem is referenced by:  rexpssxrxp  7854  rexr  7855  0xr  7856  rexrd  7859  ltrelxr  7869  iooval2  9748  fzval2  9844  seq3coll  10637  summodclem2a  11202  prodmodclem2a  11397  ismet2  12582  qtopbas  12750  tgqioo  12775
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