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Theorem ressxr 7260
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 3146 . 2  |-  RR  C_  ( RR  u.  { +oo , -oo } )
2 df-xr 7255 . 2  |-  RR*  =  ( RR  u.  { +oo , -oo } )
31, 2sseqtr4i 3042 1  |-  RR  C_  RR*
Colors of variables: wff set class
Syntax hints:    u. cun 2981    C_ wss 2983   {cpr 3418   RRcr 7078   +oocpnf 7248   -oocmnf 7249   RR*cxr 7250
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2987  df-in 2989  df-ss 2996  df-xr 7255
This theorem is referenced by:  rexpssxrxp  7261  rexr  7262  0xr  7263  rexrd  7266  ltrelxr  7276  iooval2  9050  fzval2  9144
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