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Theorem ressxr 7991
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 3298 . 2 ℝ ⊆ (ℝ ∪ {+∞, -∞})
2 df-xr 7986 . 2 * = (ℝ ∪ {+∞, -∞})
31, 2sseqtrri 3190 1 ℝ ⊆ ℝ*
Colors of variables: wff set class
Syntax hints:  cun 3127  wss 3129  {cpr 3592  cr 7801  +∞cpnf 7979  -∞cmnf 7980  *cxr 7981
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-un 3133  df-in 3135  df-ss 3142  df-xr 7986
This theorem is referenced by:  rexpssxrxp  7992  rexr  7993  0xr  7994  rexrd  7997  ltrelxr  8008  iooval2  9902  fzval2  9998  seq3coll  10806  summodclem2a  11373  prodmodclem2a  11568  ismet2  13521  qtopbas  13689  tgqioo  13714
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