Metamath Proof Explorer

Theorem xpss2

Description: Subset relation for Cartesian product. (Contributed by Jeff Hankins, 30-Aug-2009)

Ref Expression
Assertion xpss2 
|- ( A C_ B -> ( C X. A ) C_ ( C X. B ) )

Proof

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