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Theorem rexpssxrxp 9659
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

Proof of Theorem rexpssxrxp
StepHypRef Expression
1 ressxr 9658 . 2
2 xpss12 5113 . 2
31, 1, 2mp2an 672 1
Colors of variables: wff setvar class
Syntax hints:  C_wss 3475  X.cxp 5002   cr 9512   cxr 9648
This theorem is referenced by:  ltrelxr  9669  xrsdsre  21315  ovolfioo  21879  ovolficc  21880  ovolficcss  21881  ovollb  21890  ovolicc2  21933  ovolfs2  21980  uniiccdif  21987  uniioovol  21988  uniiccvol  21989  uniioombllem2  21992  uniioombllem3a  21993  uniioombllem3  21994  uniioombllem4  21995  uniioombllem5  21996  uniioombl  21998  dyadmbllem  22008  opnmbllem  22010  opnmbllem0  30050  mblfinlem1  30051  mblfinlem2  30052
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-un 3480  df-in 3482  df-ss 3489  df-opab 4511  df-xp 5010  df-xr 9653
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