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Theorem ressxr 8036
Description: The standard reals are a subset of the extended reals. (Contributed by NM, 14-Oct-2005.)
Assertion
Ref Expression
ressxr  |-  RR  C_  RR*

Proof of Theorem ressxr
StepHypRef Expression
1 ssun1 3313 . 2  |-  RR  C_  ( RR  u.  { +oo , -oo } )
2 df-xr 8031 . 2  |-  RR*  =  ( RR  u.  { +oo , -oo } )
31, 2sseqtrri 3205 1  |-  RR  C_  RR*
Colors of variables: wff set class
Syntax hints:    u. cun 3142    C_ wss 3144   {cpr 3611   RRcr 7845   +oocpnf 8024   -oocmnf 8025   RR*cxr 8026
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 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-v 2754  df-un 3148  df-in 3150  df-ss 3157  df-xr 8031
This theorem is referenced by:  rexpssxrxp  8037  rexr  8038  0xr  8039  rexrd  8042  ltrelxr  8053  iooval2  9951  fzval2  10047  seq3coll  10863  summodclem2a  11430  prodmodclem2a  11625  ismet2  14339  qtopbas  14507  tgqioo  14532
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