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Theorem ressxr 7069
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 3106 . 2  |-  RR  C_  ( RR  u.  { +oo , -oo } )
2 df-xr 7064 . 2  |-  RR*  =  ( RR  u.  { +oo , -oo } )
31, 2sseqtr4i 2978 1  |-  RR  C_  RR*
Colors of variables: wff set class
Syntax hints:    u. cun 2915    C_ wss 2917   {cpr 3376   RRcr 6888   +oocpnf 7057   -oocmnf 7058   RR*cxr 7059
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-xr 7064
This theorem is referenced by:  rexpssxrxp  7070  rexr  7071  0xr  7072  rexrd  7075  ltrelxr  7080  iooval2  8784  fzval2  8877
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