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Theorem xpss1 4536
Description: Subset relation for cross product. (Contributed by Jeff Hankins, 30-Aug-2009.)
Assertion
Ref Expression
xpss1  |-  ( A 
C_  B  ->  ( A  X.  C )  C_  ( B  X.  C
) )

Proof of Theorem xpss1
StepHypRef Expression
1 ssid 3042 . 2  |-  C  C_  C
2 xpss12 4533 . 2  |-  ( ( A  C_  B  /\  C  C_  C )  -> 
( A  X.  C
)  C_  ( B  X.  C ) )
31, 2mpan2 416 1  |-  ( A 
C_  B  ->  ( A  X.  C )  C_  ( B  X.  C
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 2997    X. cxp 4426
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-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-in 3003  df-ss 3010  df-opab 3892  df-xp 4434
This theorem is referenced by:  ssres2  4727  ssxp1  4854  funssxp  5165  tposssxp  5996  tpostpos2  6012  tfrlemibfn  6075  tfr1onlembfn  6091  tfrcllembfn  6104  enq0enq  6969
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