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Theorem ressxr 7773
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 3207 . 2 ℝ ⊆ (ℝ ∪ {+∞, -∞})
2 df-xr 7768 . 2 * = (ℝ ∪ {+∞, -∞})
31, 2sseqtrri 3100 1 ℝ ⊆ ℝ*
Colors of variables: wff set class
Syntax hints:  cun 3037  wss 3039  {cpr 3496  cr 7583  +∞cpnf 7761  -∞cmnf 7762  *cxr 7763
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 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-un 3043  df-in 3045  df-ss 3052  df-xr 7768
This theorem is referenced by:  rexpssxrxp  7774  rexr  7775  0xr  7776  rexrd  7779  ltrelxr  7789  iooval2  9649  fzval2  9744  seq3coll  10536  summodclem2a  11101  ismet2  12429  qtopbas  12597  tgqioo  12622
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