Theorem xpss2

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

	Ref	Expression
Assertion	xpss2	$$⊢A\subseteq B\to C\times A\subseteq C\times B$$

Proof

Step	Hyp	Ref	Expression
1		ssid	$$⊢C\subseteq C$$
2		xpss12	$$⊢\left(C\subseteq C\wedge A\subseteq B\right)\to C\times A\subseteq C\times B$$
3	1 2	mpan	$$⊢A\subseteq B\to C\times A\subseteq C\times B$$