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Theorem xpss2 4549
Description: Subset relation for cross product. (Contributed by Jeff Hankins, 30-Aug-2009.)
Assertion
Ref Expression
xpss2  |-  ( A 
C_  B  ->  ( C  X.  A )  C_  ( C  X.  B
) )

Proof of Theorem xpss2
StepHypRef Expression
1 ssid 3044 . 2  |-  C  C_  C
2 xpss12 4545 . 2  |-  ( ( C  C_  C  /\  A  C_  B )  -> 
( C  X.  A
)  C_  ( C  X.  B ) )
31, 2mpan 415 1  |-  ( A 
C_  B  ->  ( C  X.  A )  C_  ( C  X.  B
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 2999    X. cxp 4436
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 3005  df-ss 3012  df-opab 3900  df-xp 4444
This theorem is referenced by:  ssxp2  4868  xpdom3m  6548  axresscn  7395
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