Theorem xpeq12d

Description: Equality deduction for Cartesian product. (Contributed by NM, 8-Dec-2013)

	Ref	Expression
Hypotheses	xpeq1d.1	|- ( ph -> A = B )
	xpeq12d.2	|- ( ph -> C = D )
Assertion	xpeq12d	|- ( ph -> ( A X. C ) = ( B X. D ) )

Proof

Step	Hyp	Ref	Expression
1		xpeq1d.1	|- ( ph -> A = B )
2		xpeq12d.2	|- ( ph -> C = D )
3		xpeq12	|- ( ( A = B /\ C = D ) -> ( A X. C ) = ( B X. D ) )
4	1 2 3	syl2anc	|- ( ph -> ( A X. C ) = ( B X. D ) )