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Theorem ressxr 7963
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 3290 . 2 ℝ ⊆ (ℝ ∪ {+∞, -∞})
2 df-xr 7958 . 2 * = (ℝ ∪ {+∞, -∞})
31, 2sseqtrri 3182 1 ℝ ⊆ ℝ*
Colors of variables: wff set class
Syntax hints:  cun 3119  wss 3121  {cpr 3584  cr 7773  +∞cpnf 7951  -∞cmnf 7952  *cxr 7953
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 704  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-10 1498  ax-11 1499  ax-i12 1500  ax-bndl 1502  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152
This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-nfc 2301  df-v 2732  df-un 3125  df-in 3127  df-ss 3134  df-xr 7958
This theorem is referenced by:  rexpssxrxp  7964  rexr  7965  0xr  7966  rexrd  7969  ltrelxr  7980  iooval2  9872  fzval2  9968  seq3coll  10777  summodclem2a  11344  prodmodclem2a  11539  ismet2  13148  qtopbas  13316  tgqioo  13341
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