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Theorem xpss2 4698
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 3148 . 2  |-  C  C_  C
2 xpss12 4694 . 2  |-  ( ( C  C_  C  /\  A  C_  B )  -> 
( C  X.  A
)  C_  ( C  X.  B ) )
31, 2mpan 421 1  |-  ( A 
C_  B  ->  ( C  X.  A )  C_  ( C  X.  B
) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    C_ wss 3102    X. cxp 4585
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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-in 3108  df-ss 3115  df-opab 4027  df-xp 4593
This theorem is referenced by:  ssxp2  5024  xpdom3m  6780  axresscn  7781  tx2cn  12712  dvfvalap  13092
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