Theorem xpeq12

Description: Equality theorem for Cartesian product. (Contributed by FL, 31-Aug-2009)

	Ref	Expression
Assertion	xpeq12	$$⊢\left(A=B\wedge C=D\right)\to A\times C=B\times D$$

Proof

Step	Hyp	Ref	Expression
1		xpeq1	$$⊢A=B\to A\times C=B\times C$$
2		xpeq2	$$⊢C=D\to B\times C=B\times D$$
3	1 2	sylan9eq	$$⊢\left(A=B\wedge C=D\right)\to A\times C=B\times D$$