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Theorem rexpssxrxp 7810
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 7809 . 2  |-  RR  C_  RR*
2 xpss12 4646 . 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 3071    X. cxp 4537   RRcr 7619   RR*cxr 7799
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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-opab 3990  df-xp 4545  df-xr 7804
This theorem is referenced by:  ltrelxr  7825
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