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Theorem rexpssxrxp 7778
Description: The Cartesian product of standard reals are a subset of the Cartesian product of extended reals (common case). (Contributed by David A. Wheeler, 8-Dec-2018.)
Assertion
Ref Expression
rexpssxrxp  |-  ( RR 
X.  RR )  C_  ( RR*  X.  RR* )

Proof of Theorem rexpssxrxp
StepHypRef Expression
1 ressxr 7777 . 2  |-  RR  C_  RR*
2 xpss12 4616 . 2  |-  ( ( RR  C_  RR*  /\  RR  C_ 
RR* )  ->  ( RR  X.  RR )  C_  ( RR*  X.  RR* )
)
31, 1, 2mp2an 422 1  |-  ( RR 
X.  RR )  C_  ( RR*  X.  RR* )
Colors of variables: wff set class
Syntax hints:    C_ wss 3041    X. cxp 4507   RRcr 7587   RR*cxr 7767
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-un 3045  df-in 3047  df-ss 3054  df-opab 3960  df-xp 4515  df-xr 7772
This theorem is referenced by:  ltrelxr  7793
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