Theorem xpss2 4886

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

Step	Hyp	Ref	Expression
1		ssid 3268	. 2 |- C C_ C
2		xpss12 4882	. 2 |- ( ( C C_ C /\ A C_ B ) -> ( C X. A ) C_ ( C X. B ) )
3	1, 2	mpan 428	1 |- ( A C_ B -> ( C X. A ) C_ ( C X. B ) )

This proof depends on syntax axioms:   -> wi 4   C_ wss 3220   X. cxp 4772

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-ext 2220

This proof depends on definitions:  df-bi 117  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-in 3226  df-ss 3233  df-opab 4193  df-xp 4780

This theorem is used by:  ssxp2  5225  xpdom3m  7132  axresscn  8227  tx2cn  15371  dvfvalap  15782