Theorem xpeq1d

Description: Equality deduction for Cartesian product. (Contributed by Jeff Madsen, 17-Jun-2010)

	Ref	Expression
Hypothesis	xpeq1d.1	$$⊢\phi \to A=B$$
Assertion	xpeq1d	$$⊢\phi \to A\times C=B\times C$$

Proof

Step	Hyp	Ref	Expression
1		xpeq1d.1	$$⊢\phi \to A=B$$
2		xpeq1	$$⊢A=B\to A\times C=B\times C$$
3	1 2	syl	$$⊢\phi \to A\times C=B\times C$$