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Theorem rexpssxrxp 7530
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 7529 . 2  |-  RR  C_  RR*
2 xpss12 4545 . 2  |-  ( ( RR  C_  RR*  /\  RR  C_ 
RR* )  ->  ( RR  X.  RR )  C_  ( RR*  X.  RR* )
)
31, 1, 2mp2an 417 1  |-  ( RR 
X.  RR )  C_  ( RR*  X.  RR* )
Colors of variables: wff set class
Syntax hints:    C_ wss 2999    X. cxp 4436   RRcr 7347   RR*cxr 7519
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 3003  df-in 3005  df-ss 3012  df-opab 3900  df-xp 4444  df-xr 7524
This theorem is referenced by:  ltrelxr  7545
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