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Theorem ressxr 7127
 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 3133 . 2 ℝ ⊆ (ℝ ∪ {+∞, -∞})
2 df-xr 7122 . 2 * = (ℝ ∪ {+∞, -∞})
31, 2sseqtr4i 3005 1 ℝ ⊆ ℝ*
 Colors of variables: wff set class Syntax hints:   ∪ cun 2942   ⊆ wss 2944  {cpr 3403  ℝcr 6945  +∞cpnf 7115  -∞cmnf 7116  ℝ*cxr 7117 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-un 2949  df-in 2951  df-ss 2958  df-xr 7122 This theorem is referenced by:  rexpssxrxp  7128  rexr  7129  0xr  7130  rexrd  7133  ltrelxr  7138  iooval2  8884  fzval2  8978
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