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Theorem ressxr 7510
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 3161 . 2  |-  RR  C_  ( RR  u.  { +oo , -oo } )
2 df-xr 7505 . 2  |-  RR*  =  ( RR  u.  { +oo , -oo } )
31, 2sseqtr4i 3057 1  |-  RR  C_  RR*
Colors of variables: wff set class
Syntax hints:    u. cun 2995    C_ wss 2997   {cpr 3442   RRcr 7328   +oocpnf 7498   -oocmnf 7499   RR*cxr 7500
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-un 3001  df-in 3003  df-ss 3010  df-xr 7505
This theorem is referenced by:  rexpssxrxp  7511  rexr  7512  0xr  7513  rexrd  7516  ltrelxr  7526  iooval2  9302  fzval2  9396  iseqcoll  10212  isummolem2a  10735
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